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A first attempt to make a general scheme fo hyperbolic systems
author Ylva Rydin <ylva.rydin@telia.com>
date Fri, 16 Sep 2016 14:51:17 +0200
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children 807dfe8be3ec
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d32f674bcbe5 A first attempt to make a general scheme fo hyperbolic systems
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1 classdef hypsyst2d < scheme.Scheme
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2 properties
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3 m % Number of points in each direction, possibly a vector
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4 h % Grid spacing
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5 x,y % Grid
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6 X,Y % Values of x and y for each grid point
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7 order % Order accuracy for the approximation
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8
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9 D % non-stabalized scheme operator
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10 A, B, E
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11
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12 H % Discrete norm
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13 Hi
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14 H_x, H_y % Norms in the x and y directions
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15 Hx,Hy % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir.
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16 I_x,I_y
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17 e_w, e_e, e_s, e_n
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18 params %parameters for the coeficient matrices
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19 end
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20
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21
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22 methods
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23 function obj = hypsyst2d(m,lim,order,matrices,params)
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24
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25 xlim = lim{1};
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26 ylim = lim{2};
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27
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28 if length(m) == 1
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29 m = [m m];
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30 end
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31
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32 m_x = m(1);
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33 m_y = m(2);
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34
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35 ops_x = sbp.D2Standard(m_x,xlim,order);
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36 ops_y = sbp.D2Standard(m_y,ylim,order);
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37
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38 obj.x=ops_x.x;
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39 obj.y=ops_y.y;
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40
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41 obj.X = kr(x,ones(m_y,1));
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42 obj.Y = kr(ones(m_x,1),y);
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43
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44 I_x = speye(m_x);
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45 I_y = speye(m_y);
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46 I_n= eye(4);
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47
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48
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49 D1_x = kr(kr(I_n,ops_x.D1),I_y);
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50 obj.Hi_x= kr(kr(I_n,ops_x.HI),I_y);
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51 D1_y=kr(I_n,kr(I_x,ops_y.D1));
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52 obj.Hi_y=kr(I_n,kr(I_x,ops_y.HI));
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53
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54 obj.e_w=kr(I_n,kr(ops_x.e_l,I_y));
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55 obj.e_e=kr(I_n,kr(ops_x.e_r,I_y));
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56 obj.e_s=kr(I_n,kr(I_x,ops_y.e_l));
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57 obj.e_n=kr(I_n,kr(I_x,ops_y.e_r));
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58
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59 obj.m=m;
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60 obj.h=[ops_x.h ops_y.h];
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61 obj.order=order;
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62 obj.params=params;
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63
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64 obj.A=matrixBuild(obj,matrices.A);
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65 obj.B=matrixBuild(obj,matrices.B);
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66 obj.E=matrixBuild(obj,matrices.E);
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67
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68 obj.D=-obj.A*D1_x-obj.B*D1_y-E;
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69
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70 end
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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 % data is a function returning the data that should be applied at the boundary.
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76 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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77 % neighbour_boundary is a string specifying which boundary to interface to.
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78 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
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79 default_arg('type','neumann');
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80 default_arg('data',0);
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81
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82 switch type
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83 case{c,'char'}
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84 [tau,e_,Hi,CHM]=GetBoundarydata(obj,boundary,type);
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85 closure =Hi*e_*tau*CHM*e_';
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86 penalty =Hi*e_*tau*CHM*data;
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87 otherwise
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88 error('No such boundary condition')
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89 end
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90 end
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91
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92 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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93 error('An interface function does not exist yet');
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94 end
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95
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96 function N = size(obj)
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97 N = obj.m;
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98 end
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99
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100 end
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101
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102 methods(Static)
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103 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
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104 % and bound_v of scheme schm_v.
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105 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
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106 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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107 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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108 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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109 end
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110
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111 function [ret]=matrixBuild(obj,mat)
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112 %extra info for coordinate transfomration mult my y_ny and
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113 %x,ny osv...
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114 params=obj.params;
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115 X=obj.X;
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116 Y=obj.Y;
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117
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118 if isa(mat,'function_handle')
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119 matVec=mat(params,x,y);
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120 side=length(x);
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121 else
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122 matVec=mat;
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123 side=max(size(mat))/4;
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124 end
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125
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126
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127 ret=[diag(matVec(1,(1-1)*side+1:1*side)) diag(matVec(1,(2-1)*side+1:2*side)) diag(matVec(1,(3-1)*side+1:3*side)) diag(matVec(1,(4-1)*side+1:4*side))
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128 diag(matVec(2,(1-1)*side+1:1*side)) diag(matVec(2,(2-1)*side+1:2*side)) diag(matVec(2,(3-1)*side+1:3*side)) diag(matVec(2,(4-1)*side+1:4*side))
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129 diag(matVec(3,(1-1)*side+1:1*side)) diag(matVec(3,(2-1)*side+1:2*side)) diag(matVec(3,(3-1)*side+1:3*side)) diag(matVec(3,(4-1)*side+1:4*side))
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130 diag(matVec(4,(1-1)*side+1:1*side)) diag(matVec(4,(2-1)*side+1:2*side)) diag(matVec(4,(3-1)*side+1:3*side)) diag(matVec(4,(4-1)*side+1:4*side))];
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131 end
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132
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133 function [tau,e_,Hi, CHM]=GetBoundarydata(obj,boundary)
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134 params=obj.params;
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135 x=obj.x;
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136 y=obj.y;
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137
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138 side=max(length(x),length(y));
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139
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140
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141 switch boundary
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142 case {'w','W','west'}
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143 e_=obj.e_w;
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144 mat=obj.A;
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145 [V,D]=matrixDiag(mat,params,x(1),y);
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146 Hi=obj.Hx;
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147 tau=zeros(4*side,pos*side);
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148 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
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149 CHM=V*((D+abs(D))/2)*V';
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150 case {'e','E','east'}
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151 e_=obj.e_e;
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152 mat=obj.A;
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153 [V,D]=matrixDiag(mat,params,x(end),y);
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154 Hi=obj.Hy;
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155 tau=zeros(4*side,(4-pos));
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156 tau(pos*side+1:4*side)=-abs(D(pos*side+1:4*side,pos*side+1:4*side));
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157 CHM=V*((D-abs(D))/2)*V';
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158 case {'s','S','south'}
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159 e_=obj.e_s;
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160 mat=obj.B;
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161 [V,D]=matrixDiag(mat,params,x,y(1));
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162 Hi=obj.Hx;
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163 tau=zeros(4*side,pos*side);
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164 tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side));
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165 CHM=V*((D+abs(D))/2)*V';
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166 case {'n','N','north'}
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167 e_=obj.e_n;
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168 mat=obj.B;
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169 [V,D]=matrixDiag(mat,params,x,y(end));
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170 Hi=obj.Hy;
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171 tau=zeros(4*side,(4-pos));
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172 tau(pos*side+1:4*side)=-abs(D(pos*side+1:4*side,pos*side+1:4*side));
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173 CHM=V*((D-abs(D))/2)*V';
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174 end
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175
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176 tau=V*tau*V';
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177
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178 end
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179
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180 function [V, D,pos]=matrixDiag(mat,params,x,y)
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181 syms xs ys;
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182 [V, D]=eig(mat(params,xs,ys));
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183 xs=1;ys=1;
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184 DD=eval(diag(D));
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185
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186 pos=find(DD>=0); %Now zero eigenvalues are calculated as possitive, Maybe it should not????
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187 neg=find(DD<0);
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188 syms xs ys
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189 DD=diag(D);
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190
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191 D=diag([DD(pos); DD(neg)]);
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192 V=[V(:,pos) V(:,neg)];
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193
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194 xs=x; ys=y;
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195
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196 side=max(length(x),length(y));
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197 Dret=zeros(4,side*4);
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198 Vret=zeros(4,side*4);
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199 for ii=1:4
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200 for jj=1:4
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201 Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii));
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202 Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii));
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203 end
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204 end
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205 V=sparse(normc(Vret));
d32f674bcbe5 A first attempt to make a general scheme fo hyperbolic systems
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206 D=sparse(Dret);
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207
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208
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209 V=matrixBuild([],[],[],V);
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210 D=matrixBuild([],[],[],D);
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211 pos=legth(pos);
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212 end
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213 end
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214 end