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annotate +scheme/Beam.m @ 220:5df8d20281fe feature/beams

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Made scheme boundary_condition return a cell array of penalties if there are several of them.
author Jonatan Werpers <jonatan@werpers.com>
date Tue, 28 Jun 2016 13:11:14 +0200
parents d095b5396103
children 96dedf892910
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rev   line source
175
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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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
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9 H % Discrete norm
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10 Hi
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11
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12 e_l, e_r
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13 d1_l, d1_r
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14 d2_l, d2_r
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15 d3_l, d3_r
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16 gamm
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17 delt
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18 end
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19
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20 methods
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21 function obj = Beam(grid, order, alpha, opsGen)
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22 default_arg('alpha', 1);
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23 default_arg('opsGen', @sbp.Higher);
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24
176
d095b5396103 Fixed some bugs in Beam schemes.
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25 if ~isa(grid, 'grid.Cartesian') || grid.D() ~= 1
175
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26 error('Grid must be 1d cartesian');
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27 end
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28
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29 obj.grid = grid;
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30 obj.order = order;
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31 obj.alpha = alpha;
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32
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33 m = grid.m;
176
d095b5396103 Fixed some bugs in Beam schemes.
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34 h = grid.scaling();
175
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35
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36 ops = opsGen(m, h, order);
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37
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38 I = speye(m);
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39
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40 D4 = sparse(ops.derivatives.D4);
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41 obj.H = sparse(ops.norms.H);
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42 obj.Hi = sparse(ops.norms.HI);
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43 obj.e_l = sparse(ops.boundary.e_1);
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44 obj.e_r = sparse(ops.boundary.e_m);
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45 obj.d1_l = sparse(ops.boundary.S_1);
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46 obj.d1_r = sparse(ops.boundary.S_m);
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47 obj.d2_l = sparse(ops.boundary.S2_1);
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48 obj.d2_r = sparse(ops.boundary.S2_m);
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49 obj.d3_l = sparse(ops.boundary.S3_1);
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50 obj.d3_r = sparse(ops.boundary.S3_m);
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51
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52 obj.D = alpha*D4;
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53
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54 obj.gamm = h*ops.borrowing.N.S2/2;
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55 obj.delt = h^3*ops.borrowing.N.S3/2;
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56 end
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57
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58
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59 % Closure functions return the opertors applied to the own doamin to close the boundary
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60 % 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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61 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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62 % type is a string specifying the type of boundary condition if there are several.
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63 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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64 % neighbour_boundary is a string specifying which boundary to interface to.
220
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65 function [closure, penalty] = boundary_condition(obj,boundary,type)
175
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66 default_arg('type','dn');
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67
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68 [e, d1, d2, d3, s] = obj.get_boundary_ops(boundary);
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69 gamm = obj.gamm;
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70 delt = obj.delt;
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71
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72 switch type
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73 case {'dn'} % Dirichlet-neumann boundary condition
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74 alpha = obj.alpha;
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75
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76 % tau1 < -alpha^2/gamma
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77 % tuning = 2;
175
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78 tuning = 1.1;
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79
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80 tau1 = tuning * alpha/delt;
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81 tau4 = s*alpha;
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82
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83 sig2 = tuning * alpha/gamm;
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84 sig3 = -s*alpha;
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85
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86 tau = tau1*e+tau4*d3;
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87 sig = sig2*d1+sig3*d2;
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88
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89 closure = obj.Hi*(tau*e' + sig*d1');
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90
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91 penalty{1} = obj.Hi*tau;
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92 penalty{2} = obj.Hi*sig;
175
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93 otherwise % Unknown, boundary condition
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94 error('No such boundary condition: type = %s',type);
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95 end
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96 end
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97
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98 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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99 % u denotes the solution in the own domain
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100 % v denotes the solution in the neighbour domain
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101 [e_u,d1_u,d2_u,d3_u,s_u] = obj.get_boundary_ops(boundary);
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102 [e_v,d1_v,d2_v,d3_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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103
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104 gamm_u = obj.gamm;
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105 delt_u = obj.delt;
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106
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107 gamm_v = neighbour_scheme.gamm;
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108 delt_v = neighbour_scheme.delt;
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109
220
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110 % tuning = 2;
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111 tuning = 1.1;
175
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112
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113 alpha_u = obj.alpha;
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114 alpha_v = neighbour_scheme.alpha;
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115
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116 tau1 = ((alpha_u/2)/delt_u + (alpha_v/2)/delt_v)/2*tuning;
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117 % tau1 = (alpha_u/2 + alpha_v/2)/(2*delt_u)*tuning;
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118 tau4 = s_u*alpha_u/2;
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119
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120 sig2 = ((alpha_u/2)/gamm_u + (alpha_v/2)/gamm_v)/2*tuning;
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121 sig3 = -s_u*alpha_u/2;
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122
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123 phi2 = s_u*1/2;
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124
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125 psi1 = -s_u*1/2;
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126
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127 tau = tau1*e_u + tau4*d3_u;
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128 sig = sig2*d1_u + sig3*d2_u ;
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129 phi = phi2*d1_u ;
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130 psi = psi1*e_u ;
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131
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132 closure = obj.Hi*(tau*e_u' + sig*d1_u' + phi*alpha_u*d2_u' + psi*alpha_u*d3_u');
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133 penalty = -obj.Hi*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v');
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134 end
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135
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136 % Returns the boundary ops and sign for the boundary specified by the string boundary.
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137 % The right boundary is considered the positive boundary
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138 function [e, d1, d2, d3, s] = get_boundary_ops(obj,boundary)
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139 switch boundary
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140 case 'l'
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141 e = obj.e_l;
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142 d1 = obj.d1_l;
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143 d2 = obj.d2_l;
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144 d3 = obj.d3_l;
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145 s = -1;
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146 case 'r'
176
d095b5396103 Fixed some bugs in Beam schemes.
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147 e = obj.e_r;
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148 d1 = obj.d1_r;
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149 d2 = obj.d2_r;
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150 d3 = obj.d3_r;
175
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151 s = 1;
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152 otherwise
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153 error('No such boundary: boundary = %s',boundary);
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154 end
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155 end
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156
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157 function N = size(obj)
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158 N = prod(obj.m);
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159 end
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160
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161 end
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162 end