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annotate +sbp/D2Nonequidistant.m @ 1327:7ab7d42a5b24 feature/D2_boundary_opt

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Fix typo in comment
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 14 Feb 2022 10:49:49 +0100
parents 1b0f2415237f
children 855871e0b852
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1 classdef D2Nonequidistant < sbp.OpSet
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2 % Implements the boundary optimized variable coefficient
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3 % second derivative.
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4 %
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5 % The boundary closure uses the first and last rows of the
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6 % boundary-optimized D1 operator, i.e. the operators are
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7 % fully compatible.
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8 properties
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9 H % Norm matrix
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10 HI % H^-1
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11 D1 % SBP operator approximating first derivative
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12 D2 % SBP operator approximating second derivative
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13 DI % Dissipation operator
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14 e_l % Left boundary operator
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15 e_r % Right boundary operator
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16 d1_l % Left boundary first derivative
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17 d1_r % Right boundary first derivative
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18 m % Number of grid points.
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19 h % Step size
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20 x % grid
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21 borrowing % Struct with borrowing limits for different norm matrices
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22 options % Struct holding options used to create the operator
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23 end
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24
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25 methods
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26
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27 function obj = D2Nonequidistant(m, lim, order, options)
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28 % m - number of gridpoints
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29 % lim - cell array holding the limits of the domain
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30 % order - order of the operator
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31 % options - struct holding options used to construct the operator
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32 % struct.stencil_width: {'minimal', 'nonminimal', 'wide'}
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33 % minimal: minimal compatible stencil width (default)
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34 % nonminimal: a few additional stencil points compared to minimal
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35 % wide: wide stencil obtained by applying D1 twice
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36 % struct.AD: {'op', 'upwind'}
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37 % 'op': order-preserving AD (preserving interior stencil order) (default)
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38 % 'upwind': upwind AD (order-1 upwind interior stencil)
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39 % struct.variable_coeffs: {true, false}
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40 % true: obj.D2 is a function handle D2(c) returning a matrix
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41 % for coefficient vector c (default)
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42 % false: obj.D2 is a matrix.
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43 default_arg('options', struct);
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44 default_field(options,'stencil_width','minimal');
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45 default_field(options,'AD','op');
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46 default_field(options,'variable_coeffs',true);
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47 [x, h] = sbp.grid.accurateBoundaryOptimizedGrid(lim, m, order);
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48 switch order
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49 case 4
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50 [obj.H, obj.HI, obj.D1, obj.D2, obj.DI] = sbp.implementations.d2_noneq_variable_4(m, h, options);
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51 case 6
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52 % [obj.H, obj.HI, obj.D1, D2, M, Q, obj.e_l, obj.e_r, obj.d1_l, obj.d1_r] = sbp.implementations.d2_noneq_6(m,h,2);
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53 % obj.D2 = @(c)D2;
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54 [obj.H, obj.HI, obj.D1, obj.D2, obj.DI] = sbp.implementations.d2_noneq_variable_6(m, h, options);
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55 case 8
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56 % [obj.H, obj.HI, obj.D1, D2, M, Q, obj.e_l, obj.e_r, obj.d1_l, obj.d1_r] = sbp.implementations.d2_noneq_8(m,h,1);
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57 % obj.D2 = @(c)D2;
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58 [obj.H, obj.HI, obj.D1, obj.D2, obj.DI] = sbp.implementations.d2_noneq_variable_8(m, h, options);
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59 case 10
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60 [obj.H, obj.HI, obj.D1, obj.D2, obj.DI] = sbp.implementations.d2_noneq_variable_10(m, h, options);
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61 case 12
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62 [obj.H, obj.HI, obj.D1, obj.D2, obj.DI] = sbp.implementations.d2_noneq_variable_12(m, h, options);
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63 otherwise
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64 error('Invalid operator order %d.', order);
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65 end
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66
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67 if ~options.variable_coeffs
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68 obj.D2 = obj.D2(ones(m,1));
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69 end
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70
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71 % Boundary operators
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72 obj.e_l = sparse(m, 1); obj.e_l(1) = 1;
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73 obj.e_r = sparse(m, 1); obj.e_r(m) = 1;
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74 obj.d1_l = (obj.e_l' * obj.D1)';
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75 obj.d1_r = (obj.e_r' * obj.D1)';
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76
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77 % Borrowing coefficients
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78 obj.borrowing.H11 = obj.H(1, 1) / h; % First element in H/h,
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79 obj.borrowing.M.d1 = obj.H(1, 1) / h; % First element in H/h is borrowing also for M
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80 obj.borrowing.R.delta_D = inf;
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81
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82 % grid data
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83 obj.x = x;
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84 obj.h = h;
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85 obj.m = m;
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86
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87 % misc
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88 obj.options = options;
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89 end
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90
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91 function str = string(obj)
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92 str = [class(obj) '_' num2str(obj.order)];
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93 end
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94
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95 end
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96
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97 end