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Beam: Added ability to pick alphaII and alphaIII to control tau and sigma.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 28 Jul 2016 12:50:43 +0200
parents 8592358a3935
children 46256fffa329
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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
236
8592358a3935 Beam: Added tuning as a parameter to contructor.
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18 interface_tuning
175
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19 end
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20
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21 methods
239
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22 function obj = Beam(grid, order, alpha, opsGen, interface_tuning, alphaII, alphaIII)
236
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23 default_arg('alpha', -1);
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24 default_arg('interface_tuning', 1.1);
239
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25 default_arg('alphaII', [])
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26 default_arg('alphaIII', [])
236
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27
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443b14ea705b scheme.Beam: changes to possibly better operators.
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28 % default_arg('opsGen', @sbp.Higher);
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29 default_arg('opsGen', @sbp.HigherCompatibleVariable); % Supposed to be better
175
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30
176
d095b5396103 Fixed some bugs in Beam schemes.
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31 if ~isa(grid, 'grid.Cartesian') || grid.D() ~= 1
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32 error('Grid must be 1d cartesian');
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33 end
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34
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35 obj.grid = grid;
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36 obj.order = order;
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37 obj.alpha = alpha;
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38
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39 m = grid.m;
176
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40 h = grid.scaling();
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41
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42 ops = opsGen(m, h, order);
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43
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44 I = speye(m);
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45
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46 D4 = sparse(ops.derivatives.D4);
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47 obj.H = sparse(ops.norms.H);
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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48 obj.Hi = sparse(ops.norms.HI);
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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49 obj.e_l = sparse(ops.boundary.e_1);
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50 obj.e_r = sparse(ops.boundary.e_m);
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51 obj.d1_l = sparse(ops.boundary.S_1);
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52 obj.d1_r = sparse(ops.boundary.S_m);
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53 obj.d2_l = sparse(ops.boundary.S2_1);
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54 obj.d2_r = sparse(ops.boundary.S2_m);
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55 obj.d3_l = sparse(ops.boundary.S3_1);
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56 obj.d3_r = sparse(ops.boundary.S3_m);
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57
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58 obj.D = alpha*D4;
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59
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60 if isempty(alphaII) && isempty(alphaIII)
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61 alphaII = ops.borrowing.N.S2/2;
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62 alphaIII = ops.borrowing.N.S3/2;
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63 end
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64
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65 obj.gamm = h*alphaII;
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66 obj.delt = h^3*alphaIII;
236
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67 obj.interface_tuning = interface_tuning;
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68 end
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69
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70
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71 % Closure functions return the opertors applied to the own doamin to close the boundary
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72 % 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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73 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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74 % type is a string specifying the type of boundary condition if there are several.
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75 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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76 % neighbour_boundary is a string specifying which boundary to interface to.
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77 function [closure, penalty] = boundary_condition(obj,boundary,type)
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78 default_arg('type','dn');
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79
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80 [e, d1, d2, d3, s] = obj.get_boundary_ops(boundary);
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81 gamm = obj.gamm;
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82 delt = obj.delt;
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83
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84 switch type
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85 case {'dn'} % Dirichlet-neumann boundary condition
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86 alpha = obj.alpha;
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87
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88 % tau1 < -alpha^2/gamma
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89 % tuning = 2;
175
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90 tuning = 1.1;
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91
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92 tau1 = tuning * alpha/delt;
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93 tau4 = s*alpha;
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94
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95 sig2 = tuning * alpha/gamm;
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96 sig3 = -s*alpha;
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97
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98 tau = tau1*e+tau4*d3;
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99 sig = sig2*d1+sig3*d2;
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100
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101 closure = obj.Hi*(tau*e' + sig*d1');
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102
223
96dedf892910 Fixed sign error in beam BC penalties.
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103 penalty{1} = -obj.Hi*tau;
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104 penalty{2} = -obj.Hi*sig;
175
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105 otherwise % Unknown, boundary condition
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106 error('No such boundary condition: type = %s',type);
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107 end
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108 end
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109
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110 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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111 % u denotes the solution in the own domain
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112 % v denotes the solution in the neighbour domain
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113 [e_u,d1_u,d2_u,d3_u,s_u] = obj.get_boundary_ops(boundary);
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114 [e_v,d1_v,d2_v,d3_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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115
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116 gamm_u = obj.gamm;
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117 delt_u = obj.delt;
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118
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119 gamm_v = neighbour_scheme.gamm;
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120 delt_v = neighbour_scheme.delt;
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121
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122 tuning = obj.interface_tuning;
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123
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124
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125 alpha_u = obj.alpha;
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126 alpha_v = neighbour_scheme.alpha;
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127
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128 tau1 = ((alpha_u/2)/delt_u + (alpha_v/2)/delt_v)/2*tuning;
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129 % tau1 = (alpha_u/2 + alpha_v/2)/(2*delt_u)*tuning;
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130 tau4 = s_u*alpha_u/2;
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131
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132 sig2 = ((alpha_u/2)/gamm_u + (alpha_v/2)/gamm_v)/2*tuning;
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133 sig3 = -s_u*alpha_u/2;
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134
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135 phi2 = s_u*1/2;
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136
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137 psi1 = -s_u*1/2;
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138
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139 tau = tau1*e_u + tau4*d3_u;
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140 sig = sig2*d1_u + sig3*d2_u ;
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141 phi = phi2*d1_u ;
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142 psi = psi1*e_u ;
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143
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144 closure = obj.Hi*(tau*e_u' + sig*d1_u' + phi*alpha_u*d2_u' + psi*alpha_u*d3_u');
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145 penalty = -obj.Hi*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v');
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146 end
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147
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148 % Returns the boundary ops and sign for the boundary specified by the string boundary.
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149 % The right boundary is considered the positive boundary
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150 function [e, d1, d2, d3, s] = get_boundary_ops(obj,boundary)
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151 switch boundary
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152 case 'l'
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153 e = obj.e_l;
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154 d1 = obj.d1_l;
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155 d2 = obj.d2_l;
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156 d3 = obj.d3_l;
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157 s = -1;
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158 case 'r'
176
d095b5396103 Fixed some bugs in Beam schemes.
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159 e = obj.e_r;
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160 d1 = obj.d1_r;
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161 d2 = obj.d2_r;
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162 d3 = obj.d3_r;
175
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163 s = 1;
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164 otherwise
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165 error('No such boundary: boundary = %s',boundary);
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166 end
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167 end
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168
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169 function N = size(obj)
224
05304d7792dc Fixed type in scheme.Beam
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170 N = obj.grid.N;
175
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171 end
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172
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173 end
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174 end