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annotate +sbp/+implementations/d1_noneq_minimal_6.m @ 1031:2ef20d00b386 feature/advectionRV

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For easier comparison, return both the first order and residual viscosity when evaluating the residual. Add the first order and residual viscosity to the state of the RungekuttaRV time steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:25:06 +0100
parents f7ac3cd6eeaa
children 4cb627c7fb90
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
261
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Martin Almquist <martin.almquist@it.uu.se>
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diff changeset
1 function [D1,H,x,h] = d1_noneq_minimal_6(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<10)
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10 error('Operator requires at least 10 grid points');
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11 end
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12
261
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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 = 5;
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17 m = 2;
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18 order = 6;
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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 = 4.0842950991998e-01;
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23 x2 = 1.1968523189207e+00;
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24 x3 = 2.1968523189207e+00;
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25 x4 = 3.1968523189207e+00;
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26 x5 = 4.1968523189207e+00;
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27
267
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28 xb = sparse(m+1,1);
261
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29 for i = 0:m
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30 xb(i+1) = eval(['x' num2str(i)]);
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31 end
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32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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33
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34 %%%% Compute h %%%%%%%%%%
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35 h = L/(2*xb(end) + N-1-2*m);
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36 %%%%%%%%%%%%%%%%%%%%%%%%%
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37
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38 %%%% Define grid %%%%%%%%
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39 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
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40 %%%%%%%%%%%%%%%%%%%%%%%%%
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41
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42 %%%% Norm matrix %%%%%%%%
267
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43 P = sparse(BP,1);
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44 %#ok<*NASGU>
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45 P0 = 1.2740260779883e-01;
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46 P1 = 6.1820981002054e-01;
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47 P2 = 9.4308973897679e-01;
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48 P3 = 1.0093019060199e+00;
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49 P4 = 9.9884825610465e-01;
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50
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51 for i = 0:BP-1
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52 P(i+1) = eval(['P' num2str(i)]);
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53 end
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54
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55 H = ones(N,1);
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56 H(1:BP) = P;
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57 H(end-BP+1:end) = flip(P);
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58 H = spdiags(h*H,0,N,N);
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59 %%%%%%%%%%%%%%%%%%%%%%%%%
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60
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61 %%%% Q matrix %%%%%%%%%%%
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62
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63 % interior stencil
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64 switch order
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65 case 2
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66 d = [-1/2,0,1/2];
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67 case 4
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68 d = [1/12,-2/3,0,2/3,-1/12];
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69 case 6
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70 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
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71 case 8
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72 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
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73 case 10
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74 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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75 case 12
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76 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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77 end
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78 d = repmat(d,N,1);
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79 Q = spdiags(d,-order/2:order/2,N,N);
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80
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81 % Boundaries
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82 Q0_0 = -5.0000000000000e-01;
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83 Q0_1 = 6.3217364546846e-01;
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84 Q0_2 = -1.6411963429825e-01;
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85 Q0_3 = 3.6495407984639e-02;
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86 Q0_4 = -4.5494191548490e-03;
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87 Q0_5 = 0.0000000000000e+00;
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88 Q0_6 = 0.0000000000000e+00;
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89 Q0_7 = 0.0000000000000e+00;
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90 Q1_0 = -6.3217364546846e-01;
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91 Q1_1 = 0.0000000000000e+00;
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92 Q1_2 = 8.0515625504417e-01;
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93 Q1_3 = -2.0755653563249e-01;
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94 Q1_4 = 3.4573926056780e-02;
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95 Q1_5 = 0.0000000000000e+00;
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96 Q1_6 = 0.0000000000000e+00;
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97 Q1_7 = 0.0000000000000e+00;
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98 Q2_0 = 1.6411963429825e-01;
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99 Q2_1 = -8.0515625504417e-01;
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100 Q2_2 = 0.0000000000000e+00;
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101 Q2_3 = 7.9402676057785e-01;
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102 Q2_4 = -1.6965680649860e-01;
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103 Q2_5 = 1.6666666666667e-02;
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104 Q2_6 = 0.0000000000000e+00;
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105 Q2_7 = 0.0000000000000e+00;
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106 Q3_0 = -3.6495407984639e-02;
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107 Q3_1 = 2.0755653563249e-01;
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108 Q3_2 = -7.9402676057785e-01;
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109 Q3_3 = 0.0000000000000e+00;
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110 Q3_4 = 7.5629896626333e-01;
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111 Q3_5 = -1.5000000000000e-01;
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112 Q3_6 = 1.6666666666667e-02;
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113 Q3_7 = 0.0000000000000e+00;
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114 Q4_0 = 4.5494191548490e-03;
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115 Q4_1 = -3.4573926056780e-02;
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116 Q4_2 = 1.6965680649860e-01;
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117 Q4_3 = -7.5629896626333e-01;
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118 Q4_4 = 0.0000000000000e+00;
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119 Q4_5 = 7.5000000000000e-01;
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120 Q4_6 = -1.5000000000000e-01;
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121 Q4_7 = 1.6666666666667e-02;
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122 for i = 1:BP
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123 for j = 1:BP
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124 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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125 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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126 end
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127 end
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128 %%%%%%%%%%%%%%%%%%%%%%%%%%%
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129
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130 %%%% Difference operator %%
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131 D1 = H\Q;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
132 %%%%%%%%%%%%%%%%%%%%%%%%%%%