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annotate +scheme/Gradient.m @ 1303:49e3870335ef feature/poroelastic

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Make the hollow scheme generation more efficient by introducing the D2VariableHollow opSet
author Martin Almquist <malmquist@stanford.edu>
date Sat, 11 Jul 2020 06:54:15 -0700
parents dd25184e71ec
children
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1 classdef Gradient < scheme.Scheme
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2
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3 % Approximates the divergence
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4 % Interface and boundary condition methods are just dummies
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5
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6 properties
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7 m % Number of points in each direction, possibly a vector
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8 h % Grid spacing
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9
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10 grid
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11 dim
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12
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13 order % Order of accuracy for the approximation
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14
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15 D
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16 D1
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17 H
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18 end
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19
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20 methods
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21
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22 function obj = Gradient(g, order, opSet)
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23 default_arg('opSet',{@sbp.D2Variable, @sbp.D2Variable});
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24
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25 dim = 2;
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26
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27 m = g.size();
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28 m_tot = g.N();
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29
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30 h = g.scaling();
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31 lim = g.lim;
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32 if isempty(lim)
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33 x = g.x;
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34 lim = cell(length(x),1);
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35 for i = 1:length(x)
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36 lim{i} = {min(x{i}), max(x{i})};
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37 end
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38 end
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39
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40 % 1D operators
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41 ops = cell(dim,1);
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42 for i = 1:dim
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43 ops{i} = opSet{i}(m(i), lim{i}, order);
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44 end
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45
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46 I = cell(dim,1);
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47 D1 = cell(dim,1);
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48
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49 for i = 1:dim
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50 I{i} = speye(m(i));
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51 D1{i} = ops{i}.D1;
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52 end
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53
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54 %====== Assemble full operators ========
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55
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56 % D1
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57 obj.D1{1} = kron(D1{1},I{2});
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58 obj.D1{2} = kron(I{1},D1{2});
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59
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60 I_dim = speye(dim, dim);
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61
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62 % E{i}^T picks out component i.
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63 E = cell(dim,1);
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64 I = speye(m_tot,m_tot);
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65 for i = 1:dim
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66 e = sparse(dim,1);
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67 e(i) = 1;
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68 E{i} = kron(I,e);
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69 end
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70
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71 Grad = sparse(dim*m_tot, m_tot);
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72 for i = 1:dim
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73 Grad = Grad + E{i}*obj.D1{i};
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74 end
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75 obj.D = Grad;
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76 obj.H = [];
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77 %=========================================%'
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78
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79 end
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80
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81
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82 % Closure functions return the operators applied to the own domain to close the boundary
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83 % Penalty functions return the operators to force the solution. In the case of an interface it returns the operator applied to the other doamin.
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84 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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85 % bc is a cell array of component and bc type, e.g. {1, 'd'} for Dirichlet condition
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86 % on the first component. Can also be e.g.
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87 % {'normal', 'd'} or {'tangential', 't'} for conditions on
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88 % tangential/normal component.
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89 % data is a function returning the data that should be applied at the boundary.
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90 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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91 % neighbour_boundary is a string specifying which boundary to interface to.
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92 function [closure, penalty] = boundary_condition(obj, boundary, bc)
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93 error('Not implemented')
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94 end
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95
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96 % type Struct that specifies the interface coupling.
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97 % Fields:
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98 % -- tuning: penalty strength, defaults to 1.2
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99 % -- interpolation: type of interpolation, default 'none'
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100 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
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101
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102 [m, n] = size(obj.D);
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103 closure = sparse(m, n);
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104
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105 [m, n] = size(neighbour_scheme.D);
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106 penalty = sparse(m, n);
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107 end
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108
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109 function N = size(obj)
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110 N = obj.dim*prod(obj.m);
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111 end
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112 end
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113 end