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annotate +sbp/+implementations/d1_noneq_minimal_8.m @ 1198:2924b3a9b921 feature/d2_compatible

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Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
author Martin Almquist <malmquist@stanford.edu>
date Fri, 16 Aug 2019 14:30:28 -0700
parents f7ac3cd6eeaa
children 4cb627c7fb90
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
261
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diff changeset
1 function [D1,H,x,h] = d1_noneq_minimal_8(N,L)
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2
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3 % L: Domain length
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4 % N: Number of grid points
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5 if(nargin < 2)
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6 L = 1;
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7 end
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8
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9 if(N<12)
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10 error('Operator requires at least 12 grid points');
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11 end
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12
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13 % BP: Number of boundary points
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14 % m: Number of nonequidistant spacings
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15 % order: Accuracy of interior stencil
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16 BP = 6;
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17 m = 2;
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18 order = 8;
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19
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20 %%%% Non-equidistant grid points %%%%%
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21 x0 = 0.0000000000000e+00;
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22 x1 = 4.9439570885261e-01;
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23 x2 = 1.4051531374839e+00;
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24 x3 = 2.4051531374839e+00;
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25 x4 = 3.4051531374839e+00;
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26 x5 = 4.4051531374839e+00;
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27 x6 = 5.4051531374839e+00;
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28
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29 xb = sparse(m+1,1);
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30 for i = 0:m
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31 xb(i+1) = eval(['x' num2str(i)]);
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32 end
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33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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34
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35 %%%% Compute h %%%%%%%%%%
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36 h = L/(2*xb(end) + N-1-2*m);
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37 %%%%%%%%%%%%%%%%%%%%%%%%%
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38
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39 %%%% Define grid %%%%%%%%
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40 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
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41 %%%%%%%%%%%%%%%%%%%%%%%%%
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42
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43 %%%% Norm matrix %%%%%%%%
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44 P = sparse(BP,1);
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45 %#ok<*NASGU>
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46 P0 = 1.4523997892351e-01;
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47 P1 = 7.6864793350174e-01;
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48 P2 = 9.9116487068535e-01;
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49 P3 = 9.9992473335107e-01;
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50 P4 = 1.0002097054636e+00;
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51 P5 = 9.9996591555866e-01;
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52
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53 for i = 0:BP-1
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54 P(i+1) = eval(['P' num2str(i)]);
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55 end
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56
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57 H = ones(N,1);
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58 H(1:BP) = P;
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59 H(end-BP+1:end) = flip(P);
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60 H = spdiags(h*H,0,N,N);
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61 %%%%%%%%%%%%%%%%%%%%%%%%%
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62
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63 %%%% Q matrix %%%%%%%%%%%
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64
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65 % interior stencil
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66 switch order
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67 case 2
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68 d = [-1/2,0,1/2];
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69 case 4
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70 d = [1/12,-2/3,0,2/3,-1/12];
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71 case 6
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72 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
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73 case 8
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74 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
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75 case 10
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76 d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260];
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77 case 12
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78 d = [1/5544,-1/385,1/56,-5/63,15/56,-6/7,0,6/7,-15/56,5/63,-1/56,1/385,-1/5544];
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79 end
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80 d = repmat(d,N,1);
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81 Q = spdiags(d,-order/2:order/2,N,N);
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82
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83 % Boundaries
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84 Q0_0 = -5.0000000000000e-01;
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85 Q0_1 = 6.6697342753834e-01;
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86 Q0_2 = -2.2919342278749e-01;
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87 Q0_3 = 7.4283116457276e-02;
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88 Q0_4 = -1.2020661178873e-02;
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89 Q0_5 = -4.2460029252999e-05;
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90 Q0_6 = 0.0000000000000e+00;
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91 Q0_7 = 0.0000000000000e+00;
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92 Q0_8 = 0.0000000000000e+00;
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93 Q0_9 = 0.0000000000000e+00;
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94 Q1_0 = -6.6697342753834e-01;
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95 Q1_1 = 0.0000000000000e+00;
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96 Q1_2 = 8.8241196934163e-01;
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97 Q1_3 = -2.6653314104602e-01;
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98 Q1_4 = 5.5302527504316e-02;
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99 Q1_5 = -4.2079282615860e-03;
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100 Q1_6 = 0.0000000000000e+00;
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101 Q1_7 = 0.0000000000000e+00;
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102 Q1_8 = 0.0000000000000e+00;
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103 Q1_9 = 0.0000000000000e+00;
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104 Q2_0 = 2.2919342278749e-01;
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105 Q2_1 = -8.8241196934163e-01;
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106 Q2_2 = 0.0000000000000e+00;
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107 Q2_3 = 8.2904844081126e-01;
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108 Q2_4 = -2.1156614214635e-01;
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109 Q2_5 = 3.9307676460659e-02;
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110 Q2_6 = -3.5714285714286e-03;
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111 Q2_7 = 0.0000000000000e+00;
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112 Q2_8 = 0.0000000000000e+00;
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113 Q2_9 = 0.0000000000000e+00;
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114 Q3_0 = -7.4283116457276e-02;
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115 Q3_1 = 2.6653314104602e-01;
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116 Q3_2 = -8.2904844081126e-01;
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117 Q3_3 = 0.0000000000000e+00;
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118 Q3_4 = 8.0305501223679e-01;
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119 Q3_5 = -2.0078040553808e-01;
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120 Q3_6 = 3.8095238095238e-02;
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121 Q3_7 = -3.5714285714286e-03;
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122 Q3_8 = 0.0000000000000e+00;
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123 Q3_9 = 0.0000000000000e+00;
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124 Q4_0 = 1.2020661178873e-02;
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125 Q4_1 = -5.5302527504316e-02;
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126 Q4_2 = 2.1156614214635e-01;
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127 Q4_3 = -8.0305501223679e-01;
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128 Q4_4 = 0.0000000000000e+00;
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129 Q4_5 = 8.0024692689207e-01;
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130 Q4_6 = -2.0000000000000e-01;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
131 Q4_7 = 3.8095238095238e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
132 Q4_8 = -3.5714285714286e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
133 Q4_9 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
134 Q5_0 = 4.2460029252999e-05;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
135 Q5_1 = 4.2079282615860e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
136 Q5_2 = -3.9307676460659e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
137 Q5_3 = 2.0078040553808e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
138 Q5_4 = -8.0024692689207e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
139 Q5_5 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
140 Q5_6 = 8.0000000000000e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
141 Q5_7 = -2.0000000000000e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
142 Q5_8 = 3.8095238095238e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
143 Q5_9 = -3.5714285714286e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
144 for i = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
145 for j = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
146 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
147 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
148 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
149 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
150 %%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
151
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
152 %%%% Difference operator %%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
153 D1 = H\Q;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
154 %%%%%%%%%%%%%%%%%%%%%%%%%%%