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annotate +sbp/+implementations/d1_noneq_minimal_4.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
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1 function [D1,H,x,h] = d1_noneq_minimal_4(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<6)
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10 error('Operator requires at least 6 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 = 3;
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17 m = 1;
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18 order = 4;
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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 = 7.7122987842562e-01;
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23 x2 = 1.7712298784256e+00;
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24 x3 = 2.7712298784256e+00;
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25
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26 xb = sparse(m+1,1);
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27 for i = 0:m
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28 xb(i+1) = eval(['x' num2str(i)]);
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29 end
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30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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31
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32 %%%% Compute h %%%%%%%%%%
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33 h = L/(2*xb(end) + N-1-2*m);
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34 %%%%%%%%%%%%%%%%%%%%%%%%%
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35
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36 %%%% Define grid %%%%%%%%
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37 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
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38 %%%%%%%%%%%%%%%%%%%%%%%%%
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39
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40 %%%% Norm matrix %%%%%%%%
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41 P = sparse(BP,1);
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42 %#ok<*NASGU>
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43 P0 = 2.6864248295847e-01;
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44 P1 = 1.0094667153500e+00;
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45 P2 = 9.9312068011715e-01;
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46
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47 for i = 0:BP-1
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48 P(i+1) = eval(['P' num2str(i)]);
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49 end
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50
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51 H = ones(N,1);
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52 H(1:BP) = P;
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53 H(end-BP+1:end) = flip(P);
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54 H = spdiags(h*H,0,N,N);
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55 %%%%%%%%%%%%%%%%%%%%%%%%%
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56
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57 %%%% Q matrix %%%%%%%%%%%
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58
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59 % interior stencil
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60 switch order
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61 case 2
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62 d = [-1/2,0,1/2];
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63 case 4
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64 d = [1/12,-2/3,0,2/3,-1/12];
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65 case 6
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66 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
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67 case 8
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68 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
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69 case 10
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70 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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71 case 12
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72 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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73 end
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74 d = repmat(d,N,1);
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75 Q = spdiags(d,-order/2:order/2,N,N);
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76
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77 % Boundaries
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78 Q0_0 = -5.0000000000000e-01;
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79 Q0_1 = 6.1697245625434e-01;
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80 Q0_2 = -1.1697245625434e-01;
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81 Q0_3 = 0.0000000000000e+00;
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82 Q0_4 = 0.0000000000000e+00;
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83 Q1_0 = -6.1697245625434e-01;
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84 Q1_1 = 0.0000000000000e+00;
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85 Q1_2 = 7.0030578958767e-01;
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86 Q1_3 = -8.3333333333333e-02;
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87 Q1_4 = 0.0000000000000e+00;
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88 Q2_0 = 1.1697245625434e-01;
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89 Q2_1 = -7.0030578958767e-01;
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90 Q2_2 = 0.0000000000000e+00;
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91 Q2_3 = 6.6666666666667e-01;
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92 Q2_4 = -8.3333333333333e-02;
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93 for i = 1:BP
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94 for j = 1:BP
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95 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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96 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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97 end
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98 end
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99 %%%%%%%%%%%%%%%%%%%%%%%%%%%
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100
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101 %%%% Difference operator %%
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102 D1 = H\Q;
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103 %%%%%%%%%%%%%%%%%%%%%%%%%%%