Mercurial > repos > public > sbplib
annotate +scheme/Beam.m @ 1334:df8c71b80c33 feature/D2_boundary_opt
Use the logic grid associated with a CurvilinearGrid instead of creating a new one
author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
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date | Sat, 07 May 2022 10:40:47 +0200 |
parents | 0c504a21432d |
children |
rev | line source |
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175
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1 classdef Beam < scheme.Scheme |
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2 properties |
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3 order % Order accuracy for the approximation |
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4 grid |
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5 |
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6 D % non-stabalized scheme operator |
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7 alpha |
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8 |
242 | 9 h |
175
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10 H % Discrete norm |
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11 Hi |
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12 |
328
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13 e_l, e_r |
175
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14 d1_l, d1_r |
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15 d2_l, d2_r |
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16 d3_l, d3_r |
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17 gamm |
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18 delt |
242 | 19 alphaII |
20 alphaIII | |
240
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239
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21 |
944
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22 opt % TODO: Get rid of this and use the interface type instead |
175
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23 end |
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24 |
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25 methods |
240
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26 function obj = Beam(grid, order, alpha, opsGen, opt) |
236
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Beam: Added tuning as a parameter to contructor.
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27 default_arg('alpha', -1); |
240
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28 |
328
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29 % default_arg('opsGen', @sbp.D4); |
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30 default_arg('opsGen', @sbp.D4Variable); % Supposed to be better |
240
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31 |
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32 opt_default.interface_l.tuning = 1.1; |
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33 opt_default.interface_l.tau = []; |
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34 opt_default.interface_l.sig = []; |
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35 opt_default.interface_r.tuning = 1.1; |
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36 opt_default.interface_r.tau = []; |
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37 opt_default.interface_r.sig = []; |
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38 default_struct('opt', opt_default); |
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39 |
176
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175
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40 if ~isa(grid, 'grid.Cartesian') || grid.D() ~= 1 |
175
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41 error('Grid must be 1d cartesian'); |
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42 end |
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43 |
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44 obj.grid = grid; |
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45 obj.order = order; |
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46 obj.alpha = alpha; |
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47 |
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48 m = grid.m; |
176
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49 h = grid.scaling(); |
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50 |
328
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51 x_lim = {grid.x{1}(1), grid.x{1}(end)}; |
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52 ops = opsGen(m, x_lim, order); |
175
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53 |
328
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54 D4 = ops.D4; |
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55 obj.H = ops.H; |
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56 obj.Hi = ops.HI; |
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57 obj.e_l = ops.e_l; |
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58 obj.e_r = ops.e_r; |
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59 obj.d1_l = ops.d1_l; |
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60 obj.d1_r = ops.d1_r; |
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61 obj.d2_l = ops.d2_l; |
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62 obj.d2_r = ops.d2_r; |
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63 obj.d3_l = ops.d3_l; |
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64 obj.d3_r = ops.d3_r; |
175
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65 |
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66 obj.D = alpha*D4; |
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67 |
328
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68 alphaII = ops.borrowing.N.S2/2; |
240
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69 alphaIII = ops.borrowing.N.S3/2; |
239
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70 |
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71 obj.gamm = h*alphaII; |
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72 obj.delt = h^3*alphaIII; |
242 | 73 obj.alphaII = alphaII; |
74 obj.alphaIII = alphaIII; | |
75 obj.h = h; | |
240
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76 obj.opt = opt; |
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77 end |
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78 |
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79 |
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80 % Closure functions return the opertors applied to the own doamin to close the boundary |
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81 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. |
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82 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. |
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83 % type is a string specifying the type of boundary condition if there are several. |
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84 % neighbour_scheme is an instance of Scheme that should be interfaced to. |
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85 % neighbour_boundary is a string specifying which boundary to interface to. |
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86 function [closure, penalty] = boundary_condition(obj,boundary,type) |
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87 default_arg('type','dn'); |
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88 |
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89 e = obj.getBoundaryOperator('e', boundary); |
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90 d1 = obj.getBoundaryOperator('d1', boundary); |
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91 d2 = obj.getBoundaryOperator('d2', boundary); |
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92 d3 = obj.getBoundaryOperator('d3', boundary); |
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93 s = obj.getBoundarySign(boundary); |
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94 gamm = obj.gamm; |
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95 delt = obj.delt; |
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96 |
545 | 97 |
98 % TODO: Can this be simplifed? Can I handle conditions on u on its own, u_x on its own ... | |
99 | |
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100 switch type |
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101 case {'dn', 'clamped'} % Dirichlet-neumann boundary condition |
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102 alpha = obj.alpha; |
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103 |
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104 % tau1 < -alpha^2/gamma |
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105 % tuning = 2; |
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106 tuning = 1.1; |
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107 |
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108 tau1 = tuning * alpha/delt; |
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109 tau4 = s*alpha; |
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110 |
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111 sig2 = tuning * alpha/gamm; |
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112 sig3 = -s*alpha; |
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113 |
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114 tau = tau1*e+tau4*d3; |
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115 sig = sig2*d1+sig3*d2; |
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116 |
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117 closure = obj.Hi*(tau*e' + sig*d1'); |
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118 |
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119 penalty{1} = -obj.Hi*tau; |
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120 penalty{2} = -obj.Hi*sig; |
339
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121 |
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122 |
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123 case {'free'} |
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124 a = obj.alpha; |
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125 |
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126 tau = s*a*d1; |
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127 sig = -s*a*e; |
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128 |
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129 closure = obj.Hi*(tau*d2' + sig*d3'); |
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130 penalty{1} = -obj.Hi*tau; |
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131 penalty{2} = -obj.Hi*sig; |
339
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132 |
617
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133 case 'e' |
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134 alpha = obj.alpha; |
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135 tuning = 1.1; |
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136 |
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137 tau1 = tuning * alpha/delt; |
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138 tau4 = s*alpha; |
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139 |
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140 tau = tau1*e+tau4*d3; |
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141 |
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142 closure = obj.Hi*tau*e'; |
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143 penalty = -obj.Hi*tau; |
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144 case 'd1' |
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145 alpha = obj.alpha; |
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146 |
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147 tuning = 1.1; |
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148 |
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149 sig2 = tuning * alpha/gamm; |
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150 sig3 = -s*alpha; |
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151 |
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152 sig = sig2*d1+sig3*d2; |
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153 |
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154 closure = obj.Hi*sig*d1'; |
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155 penalty = -obj.Hi*sig; |
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156 |
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157 case 'd2' |
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158 a = obj.alpha; |
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159 |
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160 tau = s*a*d1; |
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161 |
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162 closure = obj.Hi*tau*d2'; |
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163 penalty = -obj.Hi*tau; |
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164 case 'd3' |
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165 a = obj.alpha; |
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166 |
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167 sig = -s*a*e; |
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168 |
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169 closure = obj.Hi*sig*d3'; |
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170 penalty = -obj.Hi*sig; |
339
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171 |
175
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172 otherwise % Unknown, boundary condition |
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173 error('No such boundary condition: type = %s',type); |
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174 end |
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175 end |
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176 |
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177 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary, type) |
175
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178 % u denotes the solution in the own domain |
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179 % v denotes the solution in the neighbour domain |
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180 e_u = obj.getBoundaryOperator('e', boundary); |
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181 d1_u = obj.getBoundaryOperator('d1', boundary); |
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182 d2_u = obj.getBoundaryOperator('d2', boundary); |
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183 d3_u = obj.getBoundaryOperator('d3', boundary); |
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2b1b944deae1
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184 s_u = obj.getBoundarySign(boundary); |
175
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185 |
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186 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary); |
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187 d1_v = neighbour_scheme.getBoundaryOperator('d1', neighbour_boundary); |
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188 d2_v = neighbour_scheme.getBoundaryOperator('d2', neighbour_boundary); |
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189 d3_v = neighbour_scheme.getBoundaryOperator('d3', neighbour_boundary); |
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190 s_v = neighbour_scheme.getBoundarySign(neighbour_boundary); |
175
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191 |
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192 alpha_u = obj.alpha; |
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193 alpha_v = neighbour_scheme.alpha; |
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194 |
240
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195 switch boundary |
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196 case 'l' |
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197 interface_opt = obj.opt.interface_l; |
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198 case 'r' |
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199 interface_opt = obj.opt.interface_r; |
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200 end |
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201 |
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202 |
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203 if isempty(interface_opt.tau) && isempty(interface_opt.sig) |
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204 gamm_u = obj.gamm; |
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205 delt_u = obj.delt; |
175
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206 |
240
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207 gamm_v = neighbour_scheme.gamm; |
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208 delt_v = neighbour_scheme.delt; |
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209 |
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|
210 tuning = interface_opt.tuning; |
175
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211 |
240
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|
212 tau1 = ((alpha_u/2)/delt_u + (alpha_v/2)/delt_v)/2*tuning; |
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diff
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213 sig2 = ((alpha_u/2)/gamm_u + (alpha_v/2)/gamm_v)/2*tuning; |
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diff
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|
214 else |
242 | 215 h_u = obj.h; |
216 h_v = neighbour_scheme.h; | |
217 | |
218 switch neighbour_boundary | |
219 case 'l' | |
220 neighbour_interface_opt = neighbour_scheme.opt.interface_l; | |
221 case 'r' | |
222 neighbour_interface_opt = neighbour_scheme.opt.interface_r; | |
223 end | |
224 | |
225 tau_u = interface_opt.tau; | |
226 sig_u = interface_opt.sig; | |
227 tau_v = neighbour_interface_opt.tau; | |
228 sig_v = neighbour_interface_opt.sig; | |
229 | |
230 tau1 = tau_u/h_u^3 + tau_v/h_v^3; | |
231 sig2 = sig_u/h_u + sig_v/h_v; | |
240
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diff
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|
232 end |
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|
233 |
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|
234 tau4 = s_u*alpha_u/2; |
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239
diff
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|
235 sig3 = -s_u*alpha_u/2; |
175
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|
236 phi2 = s_u*1/2; |
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|
237 psi1 = -s_u*1/2; |
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|
238 |
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diff
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|
239 tau = tau1*e_u + tau4*d3_u; |
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|
240 sig = sig2*d1_u + sig3*d2_u ; |
8f22829b69d0
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241 phi = phi2*d1_u ; |
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|
242 psi = psi1*e_u ; |
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|
243 |
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|
244 closure = obj.Hi*(tau*e_u' + sig*d1_u' + phi*alpha_u*d2_u' + psi*alpha_u*d3_u'); |
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|
245 penalty = -obj.Hi*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v'); |
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|
246 end |
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|
247 |
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
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|
248 % Returns the boundary operator op for the boundary specified by the string boundary. |
1045
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|
249 % op -- string |
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
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changeset
|
250 % boundary -- string |
1045
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|
251 function o = getBoundaryOperator(obj, op, boundary) |
1046
19ed046aec52
Clean up getBoundaryOps for a few schemes
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1045
diff
changeset
|
252 assertIsMember(op, {'e', 'd1', 'd2', 'd3'}) |
1042
8d73fcdb07a5
Add asserts to boundary identifier inputs
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998
diff
changeset
|
253 assertIsMember(boundary, {'l', 'r'}) |
998
2b1b944deae1
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changeset
|
254 |
1046
19ed046aec52
Clean up getBoundaryOps for a few schemes
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1045
diff
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255 o = obj.([op, '_', boundary]); |
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256 end |
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257 |
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258 % Returns square boundary quadrature matrix, of dimension |
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259 % corresponding to the number of boundary points |
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260 % |
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261 % boundary -- string |
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262 % Note: for 1d diffOps, the boundary quadrature is the scalar 1. |
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263 function H_b = getBoundaryQuadrature(obj, boundary) |
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264 assertIsMember(boundary, {'l', 'r'}) |
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265 |
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266 H_b = 1; |
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267 end |
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268 |
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269 % Returns the boundary sign. The right boundary is considered the positive boundary |
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270 % boundary -- string |
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271 function s = getBoundarySign(obj, boundary) |
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272 assertIsMember(boundary, {'l', 'r'}) |
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273 |
175
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274 switch boundary |
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275 case {'r'} |
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276 s = 1; |
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277 case {'l'} |
175
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278 s = -1; |
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279 end |
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280 end |
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281 |
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282 function N = size(obj) |
224
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283 N = obj.grid.N; |
175
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284 end |
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285 |
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286 end |
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287 end |