Mercurial > repos > public > sbplib
annotate +scheme/Laplace1d.m @ 1198:2924b3a9b921 feature/d2_compatible
Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
| author | Martin Almquist <malmquist@stanford.edu> |
|---|---|
| date | Fri, 16 Aug 2019 14:30:28 -0700 |
| parents | 33c378e508d2 |
| children |
| rev | line source |
|---|---|
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1 classdef Laplace1d < scheme.Scheme |
| 0 | 2 properties |
| 898 | 3 grid |
| 0 | 4 order % Order accuracy for the approximation |
| 5 | |
| 6 D % non-stabalized scheme operator | |
| 7 H % Discrete norm | |
| 8 M % Derivative norm | |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
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9 a |
| 0 | 10 |
| 11 D2 | |
| 12 Hi | |
| 13 e_l | |
| 14 e_r | |
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15 d_l |
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16 d_r |
| 0 | 17 gamm |
| 18 end | |
| 19 | |
| 20 methods | |
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21 function obj = Laplace1d(grid, order, a) |
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22 default_arg('a', 1); |
| 0 | 23 |
| 898 | 24 assertType(grid, 'grid.Cartesian'); |
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25 |
| 898 | 26 ops = sbp.D2Standard(grid.size(), grid.lim{1}, order); |
| 0 | 27 |
| 898 | 28 obj.D2 = sparse(ops.D2); |
| 29 obj.H = sparse(ops.H); | |
| 30 obj.Hi = sparse(ops.HI); | |
| 31 obj.M = sparse(ops.M); | |
| 32 obj.e_l = sparse(ops.e_l); | |
| 33 obj.e_r = sparse(ops.e_r); | |
| 34 obj.d_l = -sparse(ops.d1_l); | |
| 35 obj.d_r = sparse(ops.d1_r); | |
| 0 | 36 |
| 37 | |
| 898 | 38 obj.grid = grid; |
| 0 | 39 obj.order = order; |
| 40 | |
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41 obj.a = a; |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
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parents:
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42 obj.D = a*obj.D2; |
| 0 | 43 |
| 898 | 44 obj.gamm = grid.h*ops.borrowing.M.S; |
| 0 | 45 end |
| 46 | |
| 47 | |
| 48 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 49 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 50 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 51 % type is a string specifying the type of boundary condition if there are several. | |
| 52 % data is a function returning the data that should be applied at the boundary. | |
| 53 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 54 % neighbour_boundary is a string specifying which boundary to interface to. | |
| 55 function [closure, penalty] = boundary_condition(obj,boundary,type,data) | |
| 56 default_arg('type','neumann'); | |
| 57 default_arg('data',0); | |
| 58 | |
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59 e = obj.getBoundaryOperator('e', boundary); |
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60 d = obj.getBoundaryOperator('d', boundary); |
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Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
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61 s = obj.getBoundarySign(boundary); |
| 0 | 62 |
| 63 switch type | |
| 64 % Dirichlet boundary condition | |
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Add d and n as acceptable boundary condition identifiers, which is consistent with eg LaplaceCurvilinear.
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65 case {'D','d','dirichlet'} |
| 0 | 66 tuning = 1.1; |
| 898 | 67 tau1 = -tuning/obj.gamm; |
| 68 tau2 = 1; | |
| 0 | 69 |
| 898 | 70 tau = tau1*e + tau2*d; |
| 0 | 71 |
| 898 | 72 closure = obj.a*obj.Hi*tau*e'; |
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Bugfix minus sign in Laplace1d Dirichlet penalty.
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73 penalty = -obj.a*obj.Hi*tau; |
| 0 | 74 |
| 75 % Neumann boundary condition | |
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76 case {'N','n','neumann'} |
| 898 | 77 tau = -e; |
| 0 | 78 |
| 898 | 79 closure = obj.a*obj.Hi*tau*d'; |
| 80 penalty = -obj.a*obj.Hi*tau; | |
| 0 | 81 |
| 82 % Unknown, boundary condition | |
| 83 otherwise | |
| 84 error('No such boundary condition: type = %s',type); | |
| 85 end | |
| 86 end | |
| 87 | |
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88 function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) |
| 0 | 89 % u denotes the solution in the own domain |
| 90 % v denotes the solution in the neighbour domain | |
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91 e_u = obj.getBoundaryOperator('e', boundary); |
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92 d_u = obj.getBoundaryOperator('d', boundary); |
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Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
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parents:
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changeset
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93 s_u = obj.getBoundarySign(boundary); |
| 898 | 94 |
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95 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary); |
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96 d_v = neighbour_scheme.getBoundaryOperator('d', neighbour_boundary); |
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parents:
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diff
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97 s_v = neighbour_scheme.getBoundarySign(neighbour_boundary); |
| 0 | 98 |
| 898 | 99 a_u = obj.a; |
| 100 a_v = neighbour_scheme.a; | |
| 0 | 101 |
| 102 gamm_u = obj.gamm; | |
| 103 gamm_v = neighbour_scheme.gamm; | |
| 104 | |
| 898 | 105 tuning = 1.1; |
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106 |
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Divide interface penalty strength by 4, to make it sharp. Stability verified by eigenvalue computations.
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107 tau1 = -1/4*(a_u/gamm_u + a_v/gamm_v) * tuning; |
| 898 | 108 tau2 = 1/2*a_u; |
| 109 sig1 = -1/2; | |
| 0 | 110 sig2 = 0; |
| 111 | |
| 112 tau = tau1*e_u + tau2*d_u; | |
| 113 sig = sig1*e_u + sig2*d_u; | |
| 114 | |
| 898 | 115 closure = obj.Hi*( tau*e_u' + sig*a_u*d_u'); |
| 116 penalty = obj.Hi*(-tau*e_v' + sig*a_v*d_v'); | |
| 0 | 117 end |
| 118 | |
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119 % Returns the boundary operator op for the boundary specified by the string boundary. |
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120 % op -- string |
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121 % boundary -- string |
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122 function o = getBoundaryOperator(obj, op, boundary) |
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123 assertIsMember(op, {'e', 'd'}) |
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124 assertIsMember(boundary, {'l', 'r'}) |
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125 |
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Bugfix missing semi-colon in Laplace1d.
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126 o = obj.([op, '_', boundary]); |
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127 end |
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128 |
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129 % Returns square boundary quadrature matrix, of dimension |
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130 % corresponding to the number of boundary points |
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131 % |
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132 % boundary -- string |
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133 % Note: for 1d diffOps, the boundary quadrature is the scalar 1. |
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134 function H_b = getBoundaryQuadrature(obj, boundary) |
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135 assertIsMember(boundary, {'l', 'r'}) |
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136 |
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137 H_b = 1; |
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138 end |
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139 |
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parents:
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140 % Returns the boundary sign. The right boundary is considered the positive boundary |
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Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
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parents:
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141 % boundary -- string |
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Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
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parents:
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142 function s = getBoundarySign(obj, boundary) |
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Add asserts to boundary identifier inputs
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143 assertIsMember(boundary, {'l', 'r'}) |
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144 |
| 0 | 145 switch boundary |
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parents:
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146 case {'r'} |
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parents:
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147 s = 1; |
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Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
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parents:
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148 case {'l'} |
| 0 | 149 s = -1; |
| 150 end | |
| 151 end | |
| 152 | |
| 153 function N = size(obj) | |
| 898 | 154 N = obj.grid.size(); |
| 0 | 155 end |
| 156 | |
| 157 end | |
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Remove static method `interface_coupling` that shouldn't have existed in the first place
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158 end |