Mercurial > repos > public > sbplib

annotate +time/SBPInTime.m @ 887:50d5a3843099 feature/timesteppers

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Rename package rk4 to rk
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 15 Nov 2018 16:42:58 -0800
parents 8894e9c49e40
children f5e14e5986b5
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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365
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Martin Almquist <martin.almquist@it.uu.se>
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diff changeset
1 classdef SBPInTime < time.Timestepper
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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2 % The SBP in time method.
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3 % Implemented for v_t = A*v + f(t)
398
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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
365
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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)
406
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27
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28 default_arg('TYPE','gauss');
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29
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30 if(strcmp(TYPE,'gauss'))
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31 default_arg('order',4)
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32 default_arg('blockSize',4)
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33 else
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34 default_arg('order', 8);
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35 default_arg('blockSize',time.SBPInTime.smallestBlockSize(order,TYPE));
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36 end
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37
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38 obj.A = A;
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39 obj.f = f;
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40 obj.k_local = k/(blockSize-1);
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41 obj.k = k;
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42 obj.blockSize = blockSize;
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43 obj.t = t0;
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44 obj.m = length(v0);
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45 obj.n = 0;
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46
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47 %==== Build the time discretization matrix =====%
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48 switch TYPE
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49 case 'equidistant'
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50 ops = sbp.D2Standard(blockSize,{0,obj.k},order);
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51 case 'optimal'
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52 ops = sbp.D1Nonequidistant(blockSize,{0,obj.k},order);
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53 case 'minimal'
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54 ops = sbp.D1Nonequidistant(blockSize,{0,obj.k},order,'minimal');
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55 case 'gauss'
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56 ops = sbp.D1Gauss(blockSize,{0,obj.k});
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57 end
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58
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59 D1 = ops.D1;
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60 HI = ops.HI;
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61 e_l = ops.e_l;
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62 e_r = ops.e_r;
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63 obj.nodes = ops.x;
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64
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65 Ix = speye(size(A));
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66 It = speye(blockSize,blockSize);
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67
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68 obj.Et_r = kron(e_r,Ix);
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69
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70 % Time derivative + penalty
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71 tau = 1;
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72 Mt = D1 + tau*HI*(e_l*e_l');
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73
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74 % penalty to impose "data"
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75 penalty = tau*HI*e_l;
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76 obj.penalty = kron(penalty,Ix);
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77
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78 Mx = kron(It,A);
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79 Mt = kron(Mt,Ix);
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80 obj.M = Mt - Mx;
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81 %==============================================%
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82
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83 % LU factorization
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84 [obj.L,obj.U,obj.P,obj.Q] = lu(obj.M);
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85
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86 % Pretend that the initial condition is the last level
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87 % of a previous step.
407
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88 obj.v = 1/(e_r'*e_r) * obj.Et_r * v0;
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89
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90 end
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91
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92 function [v,t] = getV(obj)
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93 v = obj.Et_r' * obj.v;
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94 t = obj.t;
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95 end
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96
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97 function state = getState(obj)
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98 [v, t] = getV(obj);
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99 state = struct('v', v, 't', t, 'k', obj.k);
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100 end
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101
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102 function obj = step(obj)
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103 obj.v = time.sbp.sbpintime(obj.v, obj.t, obj.nodes,...
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104 obj.penalty, obj.f, obj.blockSize,...
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105 obj.Et_r,...
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106 obj.L, obj.U, obj.P, obj.Q);
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107 obj.t = obj.t + obj.k;
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108 obj.n = obj.n + 1;
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109 end
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110 end
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111
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112
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113 methods(Static)
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114 function N = smallestBlockSize(order,TYPE)
407
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115 default_arg('TYPE','gauss')
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116
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117 switch TYPE
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118
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119 case 'equidistant'
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120 switch order
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121 case 2
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122 N = 2;
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123 case 4
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124 N = 8;
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125 case 6
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126 N = 12;
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127 case 8
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128 N = 16;
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129 case 10
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130 N = 20;
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131 case 12
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132 N = 24;
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133 otherwise
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134 error('Operator does not exist');
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135 end
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136
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137 case 'optimal'
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138
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139 switch order
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140 case 4
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141 N = 8;
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142 case 6
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143 N = 12;
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144 case 8
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145 N = 16;
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146 case 10
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147 N = 20;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
148 case 12
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
149 N = 24;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
150 otherwise
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
151 error('Operator does not exist');
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
152 end
398
fccd746d8573 Refactor for clarity
Jonatan Werpers <jonatan@werpers.com>
parents: 365
diff changeset
153
365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 case 'minimal'
398
fccd746d8573 Refactor for clarity
Jonatan Werpers <jonatan@werpers.com>
parents: 365
diff changeset
155
365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
156 switch order
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
157 case 4
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
158 N = 6;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
159 case 6
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
160 N = 10;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
161 case 8
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
162 N = 12;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
163 case 10
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
164 N = 16;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
165 case 12
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
166 N = 20;
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
167 otherwise
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
168 error('Operator does not exist');
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
169 end
406
9fd9b1bea3d2 Added D1Gauss to SBPInTime
Martin Almquist <martin.almquist@it.uu.se>
parents: 398
diff changeset
170 case 'gauss'
9fd9b1bea3d2 Added D1Gauss to SBPInTime
Martin Almquist <martin.almquist@it.uu.se>
parents: 398
diff changeset
171 N = 4;
365
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
172 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
173 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
174 end
f908ce064f35 Added SBP in time timestepper.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
175 end