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annotate +scheme/Utux2D.m @ 610:b7b3c11fab4d feature/utux2D

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Add interpolation to scheme
author Martin Almquist <malmquist@stanford.edu>
date Sat, 14 Oct 2017 22:38:42 -0700
parents 0f9d20dbb7ce
children 2d85f17a8aec
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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
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11 H % Discrete norm
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12 H_x, H_y % Norms in the x and y directions
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13 Hi, Hx, Hy, Hxi, Hyi % Kroneckered norms
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14
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15 % Derivatives
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16 Dx, Dy
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17
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18 % Boundary operators
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19 e_w, e_e, e_s, e_n
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20
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21 D % Total discrete operator
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22
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23 % String, type of interface coupling
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24 % Default: 'upwind'
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25 % Other: 'centered'
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26 coupling_type
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27
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28 % String, type of interpolation operators
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29 % Default: 'AWW' (Almquist Wang Werpers)
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30 % Other: 'MC' (Mattsson Carpenter)
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31 interpolation_type
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32
591
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33
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34 end
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35
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36
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37 methods
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38 function obj = Utux2D(g ,order, opSet, a, coupling_type, interpolation_type)
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39
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40 default_arg('interpolation_type','AWW');
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41 default_arg('coupling_type','upwind');
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42 default_arg('a',1/sqrt(2)*[1, 1]);
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43 default_arg('opSet',@sbp.D2Standard);
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44 assert(isa(g, 'grid.Cartesian'))
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45
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46 m = g.size();
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47 m_x = m(1);
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48 m_y = m(2);
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49 m_tot = g.N();
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50
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51 xlim = {g.x{1}(1), g.x{1}(end)};
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52 ylim = {g.x{2}(1), g.x{2}(end)};
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53 obj.grid = g;
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54
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55 % Operator sets
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56 ops_x = opSet(m_x, xlim, order);
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57 ops_y = opSet(m_y, ylim, order);
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58 Ix = speye(m_x);
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59 Iy = speye(m_y);
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60
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61 % Norms
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62 Hx = ops_x.H;
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63 Hy = ops_y.H;
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64 Hxi = ops_x.HI;
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65 Hyi = ops_y.HI;
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66
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67 obj.H_x = Hx;
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68 obj.H_y = Hy;
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69 obj.H = kron(Hx,Hy);
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70 obj.Hi = kron(Hxi,Hyi);
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71 obj.Hx = kron(Hx,Iy);
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72 obj.Hy = kron(Ix,Hy);
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73 obj.Hxi = kron(Hxi,Iy);
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74 obj.Hyi = kron(Ix,Hyi);
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75
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76 % Derivatives
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77 Dx = ops_x.D1;
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78 Dy = ops_y.D1;
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79 obj.Dx = kron(Dx,Iy);
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80 obj.Dy = kron(Ix,Dy);
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81
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82 % Boundary operators
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83 obj.e_w = kr(ops_x.e_l, Iy);
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84 obj.e_e = kr(ops_x.e_r, Iy);
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85 obj.e_s = kr(Ix, ops_y.e_l);
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86 obj.e_n = kr(Ix, ops_y.e_r);
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87
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88 obj.m = m;
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89 obj.h = [ops_x.h ops_y.h];
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90 obj.order = order;
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91 obj.a = a;
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92 obj.coupling_type = coupling_type;
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93 obj.interpolation_type = interpolation_type;
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94 obj.D = -(a(1)*obj.Dx + a(2)*obj.Dy);
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95
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96 end
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97 % Closure functions return the opertors applied to the own domain to close the boundary
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98 % 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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99 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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100 % type is a string specifying the type of boundary condition if there are several.
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101 % data is a function returning the data that should be applied at the boundary.
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102 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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103 % neighbour_boundary is a string specifying which boundary to interface to.
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104 function [closure, penalty] = boundary_condition(obj,boundary,type)
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105 default_arg('type','dirichlet');
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106
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107 sigma = -1; % Scalar penalty parameter
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108 switch boundary
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109 case {'w','W','west','West'}
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110 tau = sigma*obj.a(1)*obj.e_w*obj.H_y;
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111 closure = obj.Hi*tau*obj.e_w';
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112
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113 case {'s','S','south','South'}
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114 tau = sigma*obj.a(2)*obj.e_s*obj.H_x;
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115 closure = obj.Hi*tau*obj.e_s';
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116 end
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117 penalty = -obj.Hi*tau;
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118
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119 end
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120
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121 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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122
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123 % Get neighbour boundary operator
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124 switch neighbour_boundary
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125 case {'e','E','east','East'}
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126 e_neighbour = neighbour_scheme.e_e;
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127 m_neighbour = neighbour_scheme.m(2);
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128 case {'w','W','west','West'}
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129 e_neighbour = neighbour_scheme.e_w;
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130 m_neighbour = neighbour_scheme.m(2);
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131 case {'n','N','north','North'}
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132 e_neighbour = neighbour_scheme.e_n;
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133 m_neighbour = neighbour_scheme.m(1);
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134 case {'s','S','south','South'}
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135 e_neighbour = neighbour_scheme.e_s;
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136 m_neighbour = neighbour_scheme.m(1);
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137 end
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138
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139 switch obj.coupling_type
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140
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141 % Upwind coupling (energy dissipation)
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142 case 'upwind'
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143 sigma_ds = -1; %"Downstream" penalty
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144 sigma_us = 0; %"Upstream" penalty
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145
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146 % Energy-preserving coupling (no energy dissipation)
0f9d20dbb7ce Add centered interface coupling in addition to upwind
Martin Almquist <malmquist@stanford.edu>
parents: 595
diff changeset
147 case 'centered'
0f9d20dbb7ce Add centered interface coupling in addition to upwind
Martin Almquist <malmquist@stanford.edu>
parents: 595
diff changeset
148 sigma_ds = -1/2; %"Downstream" penalty
0f9d20dbb7ce Add centered interface coupling in addition to upwind
Martin Almquist <malmquist@stanford.edu>
parents: 595
diff changeset
149 sigma_us = 1/2; %"Upstream" penalty
0f9d20dbb7ce Add centered interface coupling in addition to upwind
Martin Almquist <malmquist@stanford.edu>
parents: 595
diff changeset
150
0f9d20dbb7ce Add centered interface coupling in addition to upwind
Martin Almquist <malmquist@stanford.edu>
parents: 595
diff changeset
151 otherwise
0f9d20dbb7ce Add centered interface coupling in addition to upwind
Martin Almquist <malmquist@stanford.edu>
parents: 595
diff changeset
152 error(['Interface coupling type ' coupling_type ' is not available.'])
0f9d20dbb7ce Add centered interface coupling in addition to upwind
Martin Almquist <malmquist@stanford.edu>
parents: 595
diff changeset
153 end
610
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
154
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
155 % Check grid ratio for interpolation
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
156 switch boundary
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
157 case {'w','W','west','West','e','E','east','East'}
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
158 m = obj.m(2);
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
159 case {'s','S','south','South','n','N','north','North'}
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
160 m = obj.m(1);
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
161 end
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
162 grid_ratio = m/m_neighbour;
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
163 if grid_ratio ~= 1
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
164
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
165 [ms, index] = sort([m, m_neighbour]);
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
166 orders = [obj.order, neighbour_scheme.order];
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
167 orders = orders(index);
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
168
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
169 switch obj.interpolation_type
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
170 case 'MC'
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
171 interpOpSet = sbp.InterpMC(ms(1),ms(2),orders(1),orders(2));
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
172 if grid_ratio < 1
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
173 I_neighbour2local_us = interpOpSet.IF2C;
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
174 I_neighbour2local_ds = interpOpSet.IF2C;
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
175 elseif grid_ratio > 1
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
176 I_neighbour2local_us = interpOpSet.IC2F;
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
177 I_neighbour2local_ds = interpOpSet.IC2F;
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
178 end
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
179 case 'AWW'
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
180 %String 'C2F' indicates that ICF2 is more accurate.
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
181 interpOpSetF2C = sbp.InterpAWW(ms(1),ms(2),orders(1),orders(2),'F2C');
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
182 interpOpSetC2F = sbp.InterpAWW(ms(1),ms(2),orders(1),orders(2),'C2F');
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
183 if grid_ratio < 1
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
184 % Local is coarser than neighbour
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
185 I_neighbour2local_us = interpOpSetC2F.IF2C;
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
186 I_neighbour2local_ds = interpOpSetF2C.IF2C;
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
187 elseif grid_ratio > 1
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
188 % Local is finer than neighbour
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
189 I_neighbour2local_us = interpOpSetF2C.IC2F;
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
190 I_neighbour2local_ds = interpOpSetC2F.IC2F;
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
191 end
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
192 otherwise
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
193 error(['Interpolation type ' obj.interpolation_type ...
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
194 ' is not available.' ]);
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
195 end
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
196
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
197 else
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
198 % No interpolation required
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
199 I_neighbour2local_us = speye(m,m);
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
200 I_neighbour2local_ds = speye(m,m);
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
201 end
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
202
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
203 switch boundary
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
204 case {'w','W','west','West'}
595
2a2f34778ded Make Utux2D work
Martin Almquist <malmquist@stanford.edu>
parents: 591
diff changeset
205 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
206 closure = obj.Hi*tau*obj.e_w';
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
207 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour';
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
208 case {'e','E','east','East'}
595
2a2f34778ded Make Utux2D work
Martin Almquist <malmquist@stanford.edu>
parents: 591
diff changeset
209 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
210 closure = obj.Hi*tau*obj.e_e';
610
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
211 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour';
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
212 case {'s','S','south','South'}
595
2a2f34778ded Make Utux2D work
Martin Almquist <malmquist@stanford.edu>
parents: 591
diff changeset
213 tau = sigma_ds*obj.a(2)*obj.e_s*obj.H_x;
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
214 closure = obj.Hi*tau*obj.e_s';
610
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
215 penalty = -obj.Hi*tau*I_neighbour2local_ds*e_neighbour';
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
216 case {'n','N','north','North'}
595
2a2f34778ded Make Utux2D work
Martin Almquist <malmquist@stanford.edu>
parents: 591
diff changeset
217 tau = sigma_us*obj.a(2)*obj.e_n*obj.H_x;
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
218 closure = obj.Hi*tau*obj.e_n';
610
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
219 penalty = -obj.Hi*tau*I_neighbour2local_us*e_neighbour';
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
220 end
610
b7b3c11fab4d Add interpolation to scheme
Martin Almquist <malmquist@stanford.edu>
parents: 605
diff changeset
221
591
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
222
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
223 end
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
224
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
225 function N = size(obj)
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
226 N = obj.m;
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
227 end
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
228
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
229 end
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
230
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
231 methods(Static)
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
232 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
233 % and bound_v of scheme schm_v.
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
234 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
235 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
236 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
237 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
238 end
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
239 end
39554f2de783 Add Utux2D scheme
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
240 end