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annotate +scheme/Heat2dCurvilinear.m @ 1305:b5907140c069 feature/poroelastic

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Clean up hollow D2 generation by using precomputed coefficients stored in mat files
author Martin Almquist <malmquist@stanford.edu>
date Mon, 13 Jul 2020 14:21:41 -0700
parents 08f3ffe63f48
children 78db023a7fe3
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741
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
1 classdef Heat2dCurvilinear < scheme.Scheme
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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2
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
3 % Discretizes the Laplacian with variable coefficent, curvilinear,
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
4 % in the Heat equation way (i.e., the discretization matrix is not necessarily
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
5 % symmetric)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
6 % u_t = div * (kappa * grad u )
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
7 % opSet should be cell array of opSets, one per dimension. This
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
8 % is useful if we have periodic BC in one direction.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
9
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
10 properties
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
11 m % Number of points in each direction, possibly a vector
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
12 h % Grid spacing
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
13
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
14 grid
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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15 dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
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16
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
17 order % Order of accuracy for the approximation
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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18
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
19 % Diagonal matrix for variable coefficients
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
20 KAPPA % Variable coefficient
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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21
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
22 D % Total operator
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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23 D1 % First derivatives
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
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24
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
25 % Second derivatives
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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26 D2_kappa
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
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27
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
28 H, Hi % Inner products
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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29 e_l, e_r
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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30 d1_l, d1_r % Normal derivatives at the boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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31 alpha % Vector of borrowing constants
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
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32
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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33 % Boundary inner products
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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34 H_boundary_l, H_boundary_r
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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35
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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36 % Metric coefficients
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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37 b % Cell matrix of size dim x dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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38 J, Ji
742
08f3ffe63f48 Add metric scale factors to properties in heat and elastic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 741
diff changeset
39 beta % Cell array of scale factors
741
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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40
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
41 % Numerical boundary flux operators
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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42 flux_l, flux_r
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
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43
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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44 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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45
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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46 methods
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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47
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
48 function obj = Heat2dCurvilinear(g ,order, kappa_fun, opSet)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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49 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
50 default_arg('kappa_fun', @(x,y) 0*x+1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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51 dim = 2;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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52
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
53 kappa = grid.evalOn(g, kappa_fun);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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54 m = g.size();
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
55 m_tot = g.N();
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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56
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
57 % 1D operators
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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58 ops = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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59 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
60 ops{i} = opSet{i}(m(i), {0, 1}, order);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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61 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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62
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
63 I = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
64 D1 = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
65 D2 = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
66 H = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
67 Hi = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
68 e_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
69 e_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
70 d1_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
71 d1_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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72
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
73 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
74 I{i} = speye(m(i));
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
75 D1{i} = ops{i}.D1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
76 D2{i} = ops{i}.D2;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
77 H{i} = ops{i}.H;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
78 Hi{i} = ops{i}.HI;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
79 e_l{i} = ops{i}.e_l;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
80 e_r{i} = ops{i}.e_r;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
81 d1_l{i} = ops{i}.d1_l;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
82 d1_r{i} = ops{i}.d1_r;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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83 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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84
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
85 %====== Assemble full operators ========
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
86 KAPPA = spdiag(kappa);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
87 obj.KAPPA = KAPPA;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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88
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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89 % Allocate
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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90 obj.D1 = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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91 obj.D2_kappa = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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92 obj.e_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
93 obj.e_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
94 obj.d1_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
95 obj.d1_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
96
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
97 % D1
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
98 obj.D1{1} = kron(D1{1},I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
99 obj.D1{2} = kron(I{1},D1{2});
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Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
100
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
101 % -- Metric coefficients ----
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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102 coords = g.points();
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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103 x = coords(:,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
104 y = coords(:,2);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
105
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
106 % Use non-periodic difference operators for metric even if opSet is periodic.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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107 xmax = max(ops{1}.x);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
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108 ymax = max(ops{2}.x);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
109 opSetMetric{1} = sbp.D2Variable(m(1), {0, xmax}, order);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
110 opSetMetric{2} = sbp.D2Variable(m(2), {0, ymax}, order);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
111 D1Metric{1} = kron(opSetMetric{1}.D1, I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
112 D1Metric{2} = kron(I{1}, opSetMetric{2}.D1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
113
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
114 x_xi = D1Metric{1}*x;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
115 x_eta = D1Metric{2}*x;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
116 y_xi = D1Metric{1}*y;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
117 y_eta = D1Metric{2}*y;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
118
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
119 J = x_xi.*y_eta - x_eta.*y_xi;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
120
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
121 b = cell(dim,dim);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
122 b{1,1} = y_eta./J;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
123 b{1,2} = -x_eta./J;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
124 b{2,1} = -y_xi./J;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
125 b{2,2} = x_xi./J;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
126
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
127 % Scale factors for boundary integrals
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
128 beta = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
129 beta{1} = sqrt(x_eta.^2 + y_eta.^2);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
130 beta{2} = sqrt(x_xi.^2 + y_xi.^2);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
131
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
132 J = spdiag(J);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
133 Ji = inv(J);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
134 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
135 beta{i} = spdiag(beta{i});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
136 for j = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
137 b{i,j} = spdiag(b{i,j});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
138 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
139 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
140 obj.J = J;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
141 obj.Ji = Ji;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
142 obj.b = b;
742
08f3ffe63f48 Add metric scale factors to properties in heat and elastic curvilinear
Martin Almquist <malmquist@stanford.edu>
parents: 741
diff changeset
143 obj.beta = beta;
741
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
144 %----------------------------
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
145
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
146 % Boundary operators
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
147 obj.e_l{1} = kron(e_l{1},I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
148 obj.e_l{2} = kron(I{1},e_l{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
149 obj.e_r{1} = kron(e_r{1},I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
150 obj.e_r{2} = kron(I{1},e_r{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
151
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
152 obj.d1_l{1} = kron(d1_l{1},I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
153 obj.d1_l{2} = kron(I{1},d1_l{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
154 obj.d1_r{1} = kron(d1_r{1},I{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
155 obj.d1_r{2} = kron(I{1},d1_r{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
156
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
157 % D2 coefficients
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
158 kappa_coeff = cell(dim,dim);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
159 for j = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
160 obj.D2_kappa{j} = sparse(m_tot,m_tot);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
161 kappa_coeff{j} = sparse(m_tot,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
162 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
163 kappa_coeff{j} = kappa_coeff{j} + b{i,j}*J*b{i,j}*kappa;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
164 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
165 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
166 ind = grid.funcToMatrix(g, 1:m_tot);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
167
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
168 % x-dir
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
169 j = 1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
170 for col = 1:m(2)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
171 D_kappa = D2{1}(kappa_coeff{j}(ind(:,col)));
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
172
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
173 p = ind(:,col);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
174 obj.D2_kappa{j}(p,p) = D_kappa;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
175 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
176
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
177 % y-dir
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
178 j = 2;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
179 for row = 1:m(1)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
180 D_kappa = D2{2}(kappa_coeff{j}(ind(row,:)));
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
181
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
182 p = ind(row,:);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
183 obj.D2_kappa{j}(p,p) = D_kappa;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
184 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
185
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
186 % Quadratures
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
187 obj.H = kron(H{1},H{2});
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
188 obj.Hi = inv(obj.H);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
189 obj.H_boundary_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
190 obj.H_boundary_l{1} = obj.e_l{1}'*beta{1}*obj.e_l{1}*H{2};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
191 obj.H_boundary_l{2} = obj.e_l{2}'*beta{2}*obj.e_l{2}*H{1};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
192 obj.H_boundary_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
193 obj.H_boundary_r{1} = obj.e_r{1}'*beta{1}*obj.e_r{1}*H{2};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
194 obj.H_boundary_r{2} = obj.e_r{2}'*beta{2}*obj.e_r{2}*H{1};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
195
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
196 %=== Differentiation matrix D (without SAT) ===
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
197 D2_kappa = obj.D2_kappa;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
198 D1 = obj.D1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
199 D = sparse(m_tot,m_tot);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
200
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
201 d = @kroneckerDelta; % Kronecker delta
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
202 db = @(i,j) 1-d(i,j); % Logical not of Kronecker delta
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
203
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
204 % 2nd derivatives
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
205 for j = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
206 D = D + Ji*D2_kappa{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
207 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
208
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
209 % Mixed terms
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
210 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
211 for j = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
212 for k = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
213 D = D + db(i,j)*Ji*D1{j}*b{i,j}*J*KAPPA*b{i,k}*D1{k};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
214 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
215 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
216 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
217 obj.D = D;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
218 %=========================================%
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
219
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
220 % Normal flux operators for BC.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
221 flux_l = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
222 flux_r = cell(dim,1);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
223
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
224 d1_l = obj.d1_l;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
225 d1_r = obj.d1_r;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
226 e_l = obj.e_l;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
227 e_r = obj.e_r;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
228
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
229 % Loop over boundaries
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
230 for j = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
231 flux_l{j} = sparse(m_tot,m_tot);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
232 flux_r{j} = sparse(m_tot,m_tot);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
233
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
234 % Loop over dummy index
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
235 for i = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
236 % Loop over dummy index
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
237 for k = 1:dim
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
238 flux_l{j} = flux_l{j} ...
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
239 - beta{j}\b{i,j}*J*KAPPA*b{i,k}*( d(j,k)*e_l{k}*d1_l{k}' + db(j,k)*D1{k} );
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
240
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
241 flux_r{j} = flux_r{j} ...
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
242 + beta{j}\b{i,j}*J*KAPPA*b{i,k}*( d(j,k)*e_r{k}*d1_r{k}' + db(j,k)*D1{k} );
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
243 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
244
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
245 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
246 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
247 obj.flux_l = flux_l;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
248 obj.flux_r = flux_r;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
249
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
250 % Misc.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
251 obj.m = m;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
252 obj.h = g.scaling();
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
253 obj.order = order;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
254 obj.grid = g;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
255 obj.dim = dim;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
256 obj.alpha = [ops{1}.borrowing.M.d1, ops{2}.borrowing.M.d1];
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
257
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
258 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
259
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
260
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
261 % Closure functions return the operators applied to the own domain to close the boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
262 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
263 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
264 % type is a string specifying the type of boundary condition.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
265 % data is a function returning the data that should be applied at the boundary.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
266 % neighbour_scheme is an instance of Scheme that should be interfaced to.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
267 % neighbour_boundary is a string specifying which boundary to interface to.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
268 function [closure, penalty] = boundary_condition(obj, boundary, type, symmetric, tuning)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
269 default_arg('type','Neumann');
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
270 default_arg('symmetric', false);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
271 default_arg('tuning',1.2);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
272
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
273 % j is the coordinate direction of the boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
274 % nj: outward unit normal component.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
275 % nj = -1 for west, south, bottom boundaries
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
276 % nj = 1 for east, north, top boundaries
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
277 [j, nj] = obj.get_boundary_number(boundary);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
278 switch nj
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
279 case 1
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
280 e = obj.e_r{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
281 flux = obj.flux_r{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
282 H_gamma = obj.H_boundary_r{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
283 case -1
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
284 e = obj.e_l{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
285 flux = obj.flux_l{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
286 H_gamma = obj.H_boundary_l{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
287 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
288
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
289 Hi = obj.Hi;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
290 Ji = obj.Ji;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
291 KAPPA = obj.KAPPA;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
292 kappa_gamma = e'*KAPPA*e;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
293 h = obj.h(j);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
294 alpha = h*obj.alpha(j);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
295
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
296 switch type
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
297
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
298 % Dirichlet boundary condition
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
299 case {'D','d','dirichlet','Dirichlet'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
300
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
301 if ~symmetric
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
302 closure = -Ji*Hi*flux'*e*H_gamma*(e' );
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
303 penalty = Ji*Hi*flux'*e*H_gamma;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
304 else
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
305 closure = Ji*Hi*flux'*e*H_gamma*(e' )...
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
306 -tuning*2/alpha*Ji*Hi*e*kappa_gamma*H_gamma*(e' ) ;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
307 penalty = -Ji*Hi*flux'*e*H_gamma ...
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
308 +tuning*2/alpha*Ji*Hi*e*kappa_gamma*H_gamma;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
309 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
310
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
311 % Normal flux boundary condition
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
312 case {'N','n','neumann','Neumann'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
313 closure = -Ji*Hi*e*H_gamma*(e'*flux );
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
314 penalty = Ji*Hi*e*H_gamma;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
315
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
316 % Unknown boundary condition
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
317 otherwise
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
318 error('No such boundary condition: type = %s',type);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
319 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
320 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
321
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
322 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
323 % u denotes the solution in the own domain
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
324 % v denotes the solution in the neighbour domain
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
325 error('Interface not implemented');
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
326 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
327
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
328 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
329 function [j, nj] = get_boundary_number(obj, boundary)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
330
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
331 switch boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
332 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
333 j = 1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
334 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
335 j = 2;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
336 otherwise
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
337 error('No such boundary: boundary = %s',boundary);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
338 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
339
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
340 switch boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
341 case {'w','W','west','West','s','S','south','South'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
342 nj = -1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
343 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
344 nj = 1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
345 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
346 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
347
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
348 % Returns the coordinate number and outward normal component for the boundary specified by the string boundary.
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
349 function [return_op] = get_boundary_operator(obj, op, boundary)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
350
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
351 switch boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
352 case {'w','W','west','West', 'e', 'E', 'east', 'East'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
353 j = 1;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
354 case {'s','S','south','South', 'n', 'N', 'north', 'North'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
355 j = 2;
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
356 otherwise
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
357 error('No such boundary: boundary = %s',boundary);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
358 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
359
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
360 switch op
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
361 case 'e'
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
362 switch boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
363 case {'w','W','west','West','s','S','south','South'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
364 return_op = obj.e_l{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
365 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
366 return_op = obj.e_r{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
367 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
368 case 'd'
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
369 switch boundary
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
370 case {'w','W','west','West','s','S','south','South'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
371 return_op = obj.d1_l{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
372 case {'e', 'E', 'east', 'East','n', 'N', 'north', 'North'}
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
373 return_op = obj.d1_r{j};
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
374 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
375 otherwise
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
376 error(['No such operator: operatr = ' op]);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
377 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
378
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
379 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
380
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
381 function N = size(obj)
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
382 N = prod(obj.m);
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
383 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
384 end
5a9acf282b34 Add scheme Heat2Dcurvilinear. Neumann and Dirichlet seem to work. Only tested for stretched Cartesian grids though.
Martin Almquist <malmquist@stanford.edu>
parents:
diff changeset
385 end