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annotate +scheme/Utux2D.m @ 914:50cafc4b9e40 feature/utux2D

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Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
author Martin Almquist <malmquist@stanford.edu>
date Sun, 25 Nov 2018 21:09:22 -0800
parents b9c98661ff5d
children 35701c85e356
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Martin Almquist <martin.almquist@it.uu.se>
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1 classdef Utux2D < 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 grid % Grid
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6 order % Order accuracy for the approximation
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7 v0 % Initial data
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8
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9 a % Wave speed a = [a1, a2];
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10 % Can either be a constant vector or a cell array of function handles.
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11
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12 H % Discrete norm
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13 H_x, H_y % Norms in the x and y directions
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14 Hi, Hx, Hy, Hxi, Hyi % Kroneckered norms
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15
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16 % Derivatives
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17 Dx, Dy
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18
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19 % Boundary operators
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20 e_w, e_e, e_s, e_n
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21
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22 D % Total discrete operator
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23 end
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24
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25
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26 methods
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27 function obj = Utux2D(g ,order, opSet, a)
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28
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29 default_arg('a',1/sqrt(2)*[1, 1]);
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30 default_arg('opSet',@sbp.D2Standard);
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31
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32 assert(isa(g, 'grid.Cartesian'))
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33 if iscell(a)
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34 a1 = grid.evalOn(g, a{1});
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35 a2 = grid.evalOn(g, a{2});
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36 a = {spdiag(a1), spdiag(a2)};
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37 else
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38 a = {a(1), a(2)};
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39 end
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40
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41 m = g.size();
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42 m_x = m(1);
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43 m_y = m(2);
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44 m_tot = g.N();
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45
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46 xlim = {g.x{1}(1), g.x{1}(end)};
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47 ylim = {g.x{2}(1), g.x{2}(end)};
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48 obj.grid = g;
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49
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50 % Operator sets
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51 ops_x = opSet(m_x, xlim, order);
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52 ops_y = opSet(m_y, ylim, order);
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53 Ix = speye(m_x);
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54 Iy = speye(m_y);
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55
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56 % Norms
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57 Hx = ops_x.H;
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58 Hy = ops_y.H;
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59 Hxi = ops_x.HI;
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60 Hyi = ops_y.HI;
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61
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62 obj.H_x = Hx;
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63 obj.H_y = Hy;
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64 obj.H = kron(Hx,Hy);
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65 obj.Hi = kron(Hxi,Hyi);
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66 obj.Hx = kron(Hx,Iy);
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67 obj.Hy = kron(Ix,Hy);
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68 obj.Hxi = kron(Hxi,Iy);
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69 obj.Hyi = kron(Ix,Hyi);
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70
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71 % Derivatives
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72 Dx = ops_x.D1;
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73 Dy = ops_y.D1;
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74 obj.Dx = kron(Dx,Iy);
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75 obj.Dy = kron(Ix,Dy);
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76
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77 % Boundary operators
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78 obj.e_w = kr(ops_x.e_l, Iy);
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79 obj.e_e = kr(ops_x.e_r, Iy);
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80 obj.e_s = kr(Ix, ops_y.e_l);
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81 obj.e_n = kr(Ix, ops_y.e_r);
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82
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83 obj.m = m;
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84 obj.h = [ops_x.h ops_y.h];
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85 obj.order = order;
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86 obj.a = a;
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87 obj.D = -(a{1}*obj.Dx + a{2}*obj.Dy);
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88
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89 end
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90 % Closure functions return the opertors applied to the own domain to close the boundary
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91 % 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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92 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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93 % type is a string specifying the type of boundary condition if there are several.
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94 % data is a function returning the data that should be applied at the boundary.
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95 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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96 % neighbour_boundary is a string specifying which boundary to interface to.
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97 function [closure, penalty] = boundary_condition(obj,boundary,type)
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98 default_arg('type','dirichlet');
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99
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100 sigma = -1; % Scalar penalty parameter
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101 switch boundary
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102 case {'w','W','west','West'}
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103 tau = sigma*obj.a{1}*obj.e_w*obj.H_y;
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104 closure = obj.Hi*tau*obj.e_w';
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105
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106 case {'s','S','south','South'}
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107 tau = sigma*obj.a{2}*obj.e_s*obj.H_x;
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108 closure = obj.Hi*tau*obj.e_s';
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109 end
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110 penalty = -obj.Hi*tau;
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111
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112 end
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113
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114 % opts Struct that specifies the interface coupling.
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115 % Fields:
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116 % -- couplingType String, type of interface coupling
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117 % % Default: 'upwind'. Other: 'centered'
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118 % -- interpolation: struct of interpolation operators (empty for conforming grids)
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119 % -- interpolationDamping: damping on upstream and downstream sides.
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120 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,opts)
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121 if isempty(opts)
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122 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary);
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123 else
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124 assertType(opts, 'struct');
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125 if isfield(opts, 'I_local2neighbor')
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126 [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,opts);
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127 else
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128 [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,opts);
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129 end
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130 end
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131 end
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132
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133 function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,opts)
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134 default_arg('opts', struct);
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diff changeset
135 default_field(opts, 'couplingType', 'upwind');
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diff changeset
136 couplingType = opts.couplingType;
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137
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138 % Get neighbour boundary operator
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
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diff changeset
139 switch neighbour_boundary
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
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parents: 910
diff changeset
140 case {'e','E','east','East'}
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
141 e_neighbour = neighbour_scheme.e_e;
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parents: 910
diff changeset
142 case {'w','W','west','West'}
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
143 e_neighbour = neighbour_scheme.e_w;
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Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
144 case {'n','N','north','North'}
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Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
145 e_neighbour = neighbour_scheme.e_n;
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parents: 910
diff changeset
146 case {'s','S','south','South'}
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
147 e_neighbour = neighbour_scheme.e_s;
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parents: 910
diff changeset
148 end
905
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149
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diff changeset
150 switch couplingType
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151
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diff changeset
152 % Upwind coupling (energy dissipation)
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
153 case 'upwind'
605
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
154 sigma_ds = -1; %"Downstream" penalty
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Martin Almquist <malmquist@stanford.edu>
parents: 595
diff changeset
155 sigma_us = 0; %"Upstream" penalty
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diff changeset
156
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157 % Energy-preserving coupling (no energy dissipation)
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Martin Almquist <malmquist@stanford.edu>
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158 case 'centered'
605
0f9d20dbb7ce Add centered interface coupling in addition to upwind
Martin Almquist <malmquist@stanford.edu>
parents: 595
diff changeset
159 sigma_ds = -1/2; %"Downstream" penalty
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parents: 595
diff changeset
160 sigma_us = 1/2; %"Upstream" penalty
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161
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diff changeset
162 otherwise
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diff changeset
163 error(['Interface coupling type ' couplingType ' is not available.'])
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164 end
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165
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166 switch boundary
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diff changeset
167 case {'w','W','west','West'}
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diff changeset
168 tau = sigma_ds*obj.a{1}*obj.e_w*obj.H_y;
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diff changeset
169 closure = obj.Hi*tau*obj.e_w';
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diff changeset
170 penalty = -obj.Hi*tau*e_neighbour';
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diff changeset
171 case {'e','E','east','East'}
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diff changeset
172 tau = sigma_us*obj.a{1}*obj.e_e*obj.H_y;
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diff changeset
173 closure = obj.Hi*tau*obj.e_e';
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diff changeset
174 penalty = -obj.Hi*tau*e_neighbour';
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diff changeset
175 case {'s','S','south','South'}
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diff changeset
176 tau = sigma_ds*obj.a{2}*obj.e_s*obj.H_x;
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diff changeset
177 closure = obj.Hi*tau*obj.e_s';
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diff changeset
178 penalty = -obj.Hi*tau*e_neighbour';
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diff changeset
179 case {'n','N','north','North'}
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
180 tau = sigma_us*obj.a{2}*obj.e_n*obj.H_x;
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diff changeset
181 closure = obj.Hi*tau*obj.e_n';
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diff changeset
182 penalty = -obj.Hi*tau*e_neighbour';
605
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Martin Almquist <malmquist@stanford.edu>
parents: 595
diff changeset
183 end
610
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diff changeset
184
914
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diff changeset
185 end
610
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186
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diff changeset
187 function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,opts)
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diff changeset
188 default_arg('opts', struct);
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
189 default_field(opts, 'couplingType', 'upwind');
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diff changeset
190 default_field(opts, 'interpolationDamping', {0,0});
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diff changeset
191 couplingType = opts.couplingType;
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diff changeset
192 interpolationDamping = opts.interpolationDamping;
610
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diff changeset
193
914
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194 % Get neighbour boundary operator
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diff changeset
195 switch neighbour_boundary
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diff changeset
196 case {'e','E','east','East'}
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
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diff changeset
197 e_neighbour = neighbour_scheme.e_e;
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diff changeset
198 case {'w','W','west','West'}
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diff changeset
199 e_neighbour = neighbour_scheme.e_w;
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diff changeset
200 case {'n','N','north','North'}
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diff changeset
201 e_neighbour = neighbour_scheme.e_n;
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diff changeset
202 case {'s','S','south','South'}
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diff changeset
203 e_neighbour = neighbour_scheme.e_s;
905
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
Martin Almquist <malmquist@stanford.edu>
parents: 743
diff changeset
204 end
459eeb99130f Include type as (optional) input parameter in the interface method of all schemes.
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diff changeset
205
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diff changeset
206 switch couplingType
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diff changeset
207
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
208 % Upwind coupling (energy dissipation)
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
209 case 'upwind'
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
210 sigma_ds = -1; %"Downstream" penalty
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diff changeset
211 sigma_us = 0; %"Upstream" penalty
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
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diff changeset
212
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
213 % Energy-preserving coupling (no energy dissipation)
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
214 case 'centered'
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
215 sigma_ds = -1/2; %"Downstream" penalty
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
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diff changeset
216 sigma_us = 1/2; %"Upstream" penalty
666
2d85f17a8aec Add possibility for damping terms at interpolation interface.
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diff changeset
217
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diff changeset
218 otherwise
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diff changeset
219 error(['Interface coupling type ' couplingType ' is not available.'])
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
220 end
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
221
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Martin Almquist <malmquist@stanford.edu>
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diff changeset
222 int_damp_us = interpolationDamping{1};
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
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diff changeset
223 int_damp_ds = interpolationDamping{2};
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
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diff changeset
224
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
225 % u denotes the solution in the own domain
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
226 % v denotes the solution in the neighbour domain
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
227 I_local2neighbour_ds = opts.I_local2neighbor.bad;
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
228 I_local2neighbour_us = opts.I_local2neighbor.good;
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
229 I_neighbour2local_ds = opts.I_neighbor2local.good;
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
230 I_neighbour2local_us = opts.I_neighbor2local.bad;
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
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diff changeset
231
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
parents: 910
diff changeset
232 I_back_forth_us = I_neighbour2local_us*I_local2neighbour_us;
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
Martin Almquist <malmquist@stanford.edu>
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diff changeset
233 I_back_forth_ds = I_neighbour2local_ds*I_local2neighbour_ds;
666
2d85f17a8aec Add possibility for damping terms at interpolation interface.
Martin Almquist <malmquist@stanford.edu>
parents: 610
diff changeset
234
2d85f17a8aec Add possibility for damping terms at interpolation interface.
Martin Almquist <malmquist@stanford.edu>
parents: 610
diff changeset
235
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
236 switch boundary
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
237 case {'w','W','west','West'}
743
f4595f14d696 Change schemes to work for special coefficients.
Martin Almquist <malmquist@stanford.edu>
parents: 666
diff changeset
238 tau = sigma_ds*obj.a{1}*obj.e_w*obj.H_y;
610
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
239 closure = obj.Hi*tau*obj.e_w';
666
2d85f17a8aec Add possibility for damping terms at interpolation interface.
Martin Almquist <malmquist@stanford.edu>
parents: 610
diff changeset
240 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour';
2d85f17a8aec Add possibility for damping terms at interpolation interface.
Martin Almquist <malmquist@stanford.edu>
parents: 610
diff changeset
241
743
f4595f14d696 Change schemes to work for special coefficients.
Martin Almquist <malmquist@stanford.edu>
parents: 666
diff changeset
242 beta = int_damp_ds*obj.a{1}...
666
2d85f17a8aec Add possibility for damping terms at interpolation interface.
Martin Almquist <malmquist@stanford.edu>
parents: 610
diff changeset
243 *obj.e_w*obj.H_y;
914
50cafc4b9e40 Make default_field overwrite if field exists but is empty. Refactor interface method in Utux2d.
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diff changeset
244 closure = closure + obj.Hi*beta*I_back_forth_ds*obj.e_w' - obj.Hi*beta*obj.e_w';
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
245 case {'e','E','east','East'}
743
f4595f14d696 Change schemes to work for special coefficients.
Martin Almquist <malmquist@stanford.edu>
parents: 666
diff changeset
246 tau = sigma_us*obj.a{1}*obj.e_e*obj.H_y;
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
247 closure = obj.Hi*tau*obj.e_e';
610
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
248 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour';
666
2d85f17a8aec Add possibility for damping terms at interpolation interface.
Martin Almquist <malmquist@stanford.edu>
parents: 610
diff changeset
249
743
f4595f14d696 Change schemes to work for special coefficients.
Martin Almquist <malmquist@stanford.edu>
parents: 666
diff changeset
250 beta = int_damp_us*obj.a{1}...
666
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251 *obj.e_e*obj.H_y;
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252 closure = closure + obj.Hi*beta*I_back_forth_us*obj.e_e' - obj.Hi*beta*obj.e_e';
591
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253 case {'s','S','south','South'}
743
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254 tau = sigma_ds*obj.a{2}*obj.e_s*obj.H_x;
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255 closure = obj.Hi*tau*obj.e_s';
610
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256 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour';
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257
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258 beta = int_damp_ds*obj.a{2}...
666
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259 *obj.e_s*obj.H_x;
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260 closure = closure + obj.Hi*beta*I_back_forth_ds*obj.e_s' - obj.Hi*beta*obj.e_s';
591
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261 case {'n','N','north','North'}
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262 tau = sigma_us*obj.a{2}*obj.e_n*obj.H_x;
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263 closure = obj.Hi*tau*obj.e_n';
610
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parents: 605
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264 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour';
666
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265
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266 beta = int_damp_us*obj.a{2}...
666
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267 *obj.e_n*obj.H_x;
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268 closure = closure + obj.Hi*beta*I_back_forth_us*obj.e_n' - obj.Hi*beta*obj.e_n';
591
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269 end
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270
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271
591
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272 end
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273
591
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274 function N = size(obj)
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275 N = obj.m;
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276 end
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277
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278 end
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279
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280 methods(Static)
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281 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
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282 % and bound_v of scheme schm_v.
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283 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
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284 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
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285 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
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286 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
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287 end
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288 end
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289 end