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annotate +time/SBPInTime.m @ 401:9ff24a14f9ef feature/beams

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Merge clarity changes for SBPInTime.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 02 Feb 2017 10:07:49 +0100
parents 14f2be4fe9c1 fccd746d8573
children 38173ea263ed
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Martin Almquist <martin.almquist@it.uu.se>
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1 classdef SBPInTime < time.Timestepper
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2 % The SBP in time method.
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3 % Implemented for v_t = A*v + f(t)
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4 %
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5 % Each "step" takes one block step and thus advances
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6 % k = k_local*(blockSize-1) in time.
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7 properties
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8 M % System matrix
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9 L,U,P,Q % LU factorization of M
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10 A
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11 Et_r
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12 penalty
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13 f
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14 k_local % step size within a block
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15 k % Time size of a block k/(blockSize-1) = k_local
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16 t
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17 v
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18 m
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19 n
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20 blockSize % number of points in each block
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21 order
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22 nodes
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23 end
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24
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25 methods
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26 function obj = SBPInTime(A, f, k, t0, v0, TYPE, order, blockSize)
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27 default_arg('TYPE','minimal');
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28 default_arg('order', 8);
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29 default_arg('blockSize',time.SBPInTime.smallestBlockSize(order,TYPE));
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30
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31 obj.A = A;
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32 obj.f = f;
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33 obj.k_local = k/(blockSize-1);
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34 obj.k = k;
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35 obj.blockSize = blockSize;
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36 obj.t = t0;
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37 obj.m = length(v0);
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38 obj.n = 0;
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39
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40 %==== Build the time discretization matrix =====%
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41 switch TYPE
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42 case 'equidistant'
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43 ops = sbp.D2Standard(blockSize,{0,obj.k},order);
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44 case 'optimal'
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45 ops = sbp.D1Nonequidistant(blockSize,{0,obj.k},order);
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46 case 'minimal'
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47 ops = sbp.D1Nonequidistant(blockSize,{0,obj.k},order,'minimal');
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48 end
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49
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50 D1 = ops.D1;
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51 HI = ops.HI;
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52 e_l = ops.e_l;
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53 e_r = ops.e_r;
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54 obj.nodes = ops.x;
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55
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56 Ix = speye(size(A));
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57 It = speye(blockSize,blockSize);
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58
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59 obj.Et_r = kron(e_r,Ix);
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60
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61 % Time derivative + penalty
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62 tau = 1;
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63 Mt = D1 + tau*HI*(e_l*e_l');
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64
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65 % penalty to impose "data"
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66 penalty = tau*HI*e_l;
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67 obj.penalty = kron(penalty,Ix);
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68
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69 Mx = kron(It,A);
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70 Mt = kron(Mt,Ix);
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71 obj.M = Mt - Mx;
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72 %==============================================%
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73
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74 % LU factorization
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75 [obj.L,obj.U,obj.P,obj.Q] = lu(obj.M);
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76
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77 % Pretend that the initial condition is the last level
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78 % of a previous step.
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79 obj.v = obj.Et_r * v0;
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80
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81 end
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82
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83 function [v,t] = getV(obj)
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84 v = obj.Et_r' * obj.v;
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85 t = obj.t;
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86 end
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87
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88 function obj = step(obj)
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89 obj.v = time.sbp.sbpintime(obj.v, obj.t, obj.nodes,...
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90 obj.penalty, obj.f, obj.blockSize,...
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91 obj.Et_r,...
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92 obj.L, obj.U, obj.P, obj.Q);
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93 obj.t = obj.t + obj.k;
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94 obj.n = obj.n + 1;
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95 end
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96 end
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97
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98
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99 methods(Static)
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100 function N = smallestBlockSize(order,TYPE)
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101 default_arg('TYPE','equidistant')
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102
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103 switch TYPE
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104
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105 case 'equidistant'
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106 switch order
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107 case 2
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108 N = 2;
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109 case 4
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110 N = 8;
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111 case 6
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112 N = 12;
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113 case 8
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114 N = 16;
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115 case 10
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116 N = 20;
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117 case 12
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118 N = 24;
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119 otherwise
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120 error('Operator does not exist');
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121 end
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122
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123 case 'optimal'
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124
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125 switch order
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126 case 4
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127 N = 8;
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128 case 6
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129 N = 12;
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130 case 8
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131 N = 16;
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132 case 10
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133 N = 20;
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134 case 12
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135 N = 24;
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136 otherwise
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137 error('Operator does not exist');
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138 end
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139
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140 case 'minimal'
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141
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142 switch order
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143 case 4
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144 N = 6;
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145 case 6
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146 N = 10;
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147 case 8
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148 N = 12;
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149 case 10
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150 N = 16;
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151 case 12
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152 N = 20;
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diff changeset
153 otherwise
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 error('Operator does not exist');
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
155 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
156 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
157 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
158 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
159 end