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annotate +sbp/+implementations/d1_noneq_6.m @ 1037:2d7ba44340d0 feature/burgers1d

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Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 18 Jan 2019 09:02:02 +0100
parents f7ac3cd6eeaa
children 4cb627c7fb90
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
261
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1 function [D1,H,x,h] = d1_noneq_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<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 = 3;
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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 = 4.4090263368623e-01;
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23 x2 = 1.2855984345073e+00;
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24 x3 = 2.2638953951239e+00;
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25 x4 = 3.2638953951239e+00;
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26 x5 = 4.2638953951239e+00;
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27 x6 = 5.2638953951239e+00;
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28
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29 xb = sparse(m+1,1);
261
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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 = 1.3030223027124e-01;
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47 P1 = 6.8851501587715e-01;
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48 P2 = 9.5166202564389e-01;
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49 P3 = 9.9103890475697e-01;
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50 P4 = 1.0028757074552e+00;
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51 P5 = 9.9950151111941e-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 = 6.6042071945824e-01;
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86 Q0_2 = -2.2104152954203e-01;
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87 Q0_3 = 7.6243679810093e-02;
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88 Q0_4 = -1.7298206716724e-02;
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89 Q0_5 = 1.6753369904210e-03;
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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 Q1_0 = -6.6042071945824e-01;
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94 Q1_1 = 0.0000000000000e+00;
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95 Q1_2 = 8.7352798702787e-01;
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96 Q1_3 = -2.6581719253084e-01;
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97 Q1_4 = 5.7458484948314e-02;
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98 Q1_5 = -4.7485599871040e-03;
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99 Q1_6 = 0.0000000000000e+00;
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100 Q1_7 = 0.0000000000000e+00;
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101 Q1_8 = 0.0000000000000e+00;
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102 Q2_0 = 2.2104152954203e-01;
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103 Q2_1 = -8.7352798702787e-01;
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104 Q2_2 = 0.0000000000000e+00;
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105 Q2_3 = 8.1707122038457e-01;
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106 Q2_4 = -1.8881125503769e-01;
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107 Q2_5 = 2.4226492138960e-02;
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108 Q2_6 = 0.0000000000000e+00;
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109 Q2_7 = 0.0000000000000e+00;
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110 Q2_8 = 0.0000000000000e+00;
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111 Q3_0 = -7.6243679810093e-02;
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112 Q3_1 = 2.6581719253084e-01;
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113 Q3_2 = -8.1707122038457e-01;
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114 Q3_3 = 0.0000000000000e+00;
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115 Q3_4 = 7.6798636652679e-01;
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116 Q3_5 = -1.5715532552963e-01;
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117 Q3_6 = 1.6666666666667e-02;
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118 Q3_7 = 0.0000000000000e+00;
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119 Q3_8 = 0.0000000000000e+00;
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120 Q4_0 = 1.7298206716724e-02;
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121 Q4_1 = -5.7458484948314e-02;
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122 Q4_2 = 1.8881125503769e-01;
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123 Q4_3 = -7.6798636652679e-01;
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124 Q4_4 = 0.0000000000000e+00;
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125 Q4_5 = 7.5266872305402e-01;
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126 Q4_6 = -1.5000000000000e-01;
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127 Q4_7 = 1.6666666666667e-02;
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128 Q4_8 = 0.0000000000000e+00;
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129 Q5_0 = -1.6753369904210e-03;
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130 Q5_1 = 4.7485599871040e-03;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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131 Q5_2 = -2.4226492138960e-02;
6009f2712d13 Moved and renamned all implementations.
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132 Q5_3 = 1.5715532552963e-01;
6009f2712d13 Moved and renamned all implementations.
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133 Q5_4 = -7.5266872305402e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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diff changeset
134 Q5_5 = 0.0000000000000e+00;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
135 Q5_6 = 7.5000000000000e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
136 Q5_7 = -1.5000000000000e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
137 Q5_8 = 1.6666666666667e-02;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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138 for i = 1:BP
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Martin Almquist <martin.almquist@it.uu.se>
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diff changeset
139 for j = 1:BP
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
140 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
141 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
142 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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143 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
144 %%%%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
145
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
146 %%%% Difference operator %%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
147 D1 = H\Q;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
148 %%%%%%%%%%%%%%%%%%%%%%%%%%%