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annotate +sbp/+implementations/d1_noneq_4.m @ 261:6009f2712d13 operator_remake

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Moved and renamned all implementations.
author Martin Almquist <martin.almquist@it.uu.se>
date Thu, 08 Sep 2016 15:35:45 +0200
parents
children bfa130b7abf6
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261
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
1 function [D1,H,x,h] = d1_noneq_4(N,L)
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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2
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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3 % L: Domain length
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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4 % N: Number of grid points
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Martin Almquist <martin.almquist@it.uu.se>
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5 if(nargin < 2)
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Martin Almquist <martin.almquist@it.uu.se>
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6 L = 1;
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Martin Almquist <martin.almquist@it.uu.se>
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7 end
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Martin Almquist <martin.almquist@it.uu.se>
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8
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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9 % BP: Number of boundary points
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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10 % m: Number of nonequidistant spacings
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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11 % order: Accuracy of interior stencil
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Martin Almquist <martin.almquist@it.uu.se>
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12 BP = 4;
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Martin Almquist <martin.almquist@it.uu.se>
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13 m = 2;
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Martin Almquist <martin.almquist@it.uu.se>
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14 order = 4;
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Martin Almquist <martin.almquist@it.uu.se>
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15
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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16 %%%% Non-equidistant grid points %%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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17 x0 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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18 x1 = 6.8764546205559e-01;
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Martin Almquist <martin.almquist@it.uu.se>
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19 x2 = 1.8022115125776e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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20 x3 = 2.8022115125776e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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21 x4 = 3.8022115125776e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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22
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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23 xb = zeros(m+1,1);
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Martin Almquist <martin.almquist@it.uu.se>
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24 for i = 0:m
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Martin Almquist <martin.almquist@it.uu.se>
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25 xb(i+1) = eval(['x' num2str(i)]);
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Martin Almquist <martin.almquist@it.uu.se>
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26 end
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Martin Almquist <martin.almquist@it.uu.se>
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27 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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28
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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29 %%%% Compute h %%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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30 h = L/(2*xb(end) + N-1-2*m);
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Martin Almquist <martin.almquist@it.uu.se>
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31 %%%%%%%%%%%%%%%%%%%%%%%%%
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32
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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33 %%%% Define grid %%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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34 x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ];
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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35 %%%%%%%%%%%%%%%%%%%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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36
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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37 %%%% Norm matrix %%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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38 P = zeros(BP,1);
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Martin Almquist <martin.almquist@it.uu.se>
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39 %#ok<*NASGU>
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Martin Almquist <martin.almquist@it.uu.se>
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40 P0 = 2.1259737557798e-01;
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Martin Almquist <martin.almquist@it.uu.se>
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41 P1 = 1.0260290400758e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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42 P2 = 1.0775123588954e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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43 P3 = 9.8607273802835e-01;
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44
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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45 for i = 0:BP-1
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Martin Almquist <martin.almquist@it.uu.se>
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46 P(i+1) = eval(['P' num2str(i)]);
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Martin Almquist <martin.almquist@it.uu.se>
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47 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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48
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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49 H = ones(N,1);
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Martin Almquist <martin.almquist@it.uu.se>
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50 H(1:BP) = P;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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51 H(end-BP+1:end) = flip(P);
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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52 H = spdiags(h*H,0,N,N);
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Martin Almquist <martin.almquist@it.uu.se>
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53 %%%%%%%%%%%%%%%%%%%%%%%%%
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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54
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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55 %%%% Q matrix %%%%%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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56
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Martin Almquist <martin.almquist@it.uu.se>
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57 % interior stencil
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Martin Almquist <martin.almquist@it.uu.se>
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58 switch order
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Martin Almquist <martin.almquist@it.uu.se>
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59 case 2
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Martin Almquist <martin.almquist@it.uu.se>
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60 d = [-1/2,0,1/2];
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Martin Almquist <martin.almquist@it.uu.se>
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61 case 4
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Martin Almquist <martin.almquist@it.uu.se>
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62 d = [1/12,-2/3,0,2/3,-1/12];
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Martin Almquist <martin.almquist@it.uu.se>
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63 case 6
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Martin Almquist <martin.almquist@it.uu.se>
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64 d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60];
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Martin Almquist <martin.almquist@it.uu.se>
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65 case 8
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Martin Almquist <martin.almquist@it.uu.se>
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66 d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280];
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Martin Almquist <martin.almquist@it.uu.se>
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67 case 10
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Martin Almquist <martin.almquist@it.uu.se>
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68 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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Martin Almquist <martin.almquist@it.uu.se>
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69 case 12
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Martin Almquist <martin.almquist@it.uu.se>
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70 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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Martin Almquist <martin.almquist@it.uu.se>
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71 end
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
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72 d = repmat(d,N,1);
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Martin Almquist <martin.almquist@it.uu.se>
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73 Q = spdiags(d,-order/2:order/2,N,N);
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Martin Almquist <martin.almquist@it.uu.se>
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74
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Martin Almquist <martin.almquist@it.uu.se>
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75 % Boundaries
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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76 Q0_0 = -5.0000000000000e-01;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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77 Q0_1 = 6.5605279837843e-01;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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78 Q0_2 = -1.9875859409017e-01;
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79 Q0_3 = 4.2705795711740e-02;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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80 Q0_4 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
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81 Q0_5 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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82 Q1_0 = -6.5605279837843e-01;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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83 Q1_1 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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84 Q1_2 = 8.1236966439895e-01;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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85 Q1_3 = -1.5631686602052e-01;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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86 Q1_4 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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87 Q1_5 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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88 Q2_0 = 1.9875859409017e-01;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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89 Q2_1 = -8.1236966439895e-01;
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Martin Almquist <martin.almquist@it.uu.se>
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90 Q2_2 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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91 Q2_3 = 6.9694440364211e-01;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
92 Q2_4 = -8.3333333333333e-02;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
93 Q2_5 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
94 Q3_0 = -4.2705795711740e-02;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
95 Q3_1 = 1.5631686602052e-01;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
96 Q3_2 = -6.9694440364211e-01;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
diff changeset
97 Q3_3 = 0.0000000000000e+00;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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98 Q3_4 = 6.6666666666667e-01;
6009f2712d13 Moved and renamned all implementations.
Martin Almquist <martin.almquist@it.uu.se>
parents:
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99 Q3_5 = -8.3333333333333e-02;
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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100 for i = 1:BP
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Martin Almquist <martin.almquist@it.uu.se>
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101 for j = 1:BP
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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102 Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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103 Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]);
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Martin Almquist <martin.almquist@it.uu.se>
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104 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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105 end
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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106 %%%%%%%%%%%%%%%%%%%%%%%%%%%
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Martin Almquist <martin.almquist@it.uu.se>
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107
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Martin Almquist <martin.almquist@it.uu.se>
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108 %%%% Difference operator %%
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Martin Almquist <martin.almquist@it.uu.se>
parents:
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109 D1 = H\Q;
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Martin Almquist <martin.almquist@it.uu.se>
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110 %%%%%%%%%%%%%%%%%%%%%%%%%%%