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annotate +sbp/+implementations/d4_variable_2.m @ 1203:25cadc69a589 feature/poroelastic

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Update comments in Anisotropic
author Martin Almquist <malmquist@stanford.edu>
date Thu, 05 Sep 2019 17:10:58 -0700
parents 43d02533bea3
children
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1 % Returns D2 as a function handle
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2 function [H, HI, D1, D2, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = d4_variable_2(m,h)
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3 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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4 %%% 4:de ordn. SBP Finita differens %%%
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5 %%% operatorer framtagna av Ken Mattsson %%%
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6 %%% %%%
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7 %%% 6 randpunkter, diagonal norm %%%
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8 %%% %%%
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9 %%% Datum: 2013-11-11 %%%
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10 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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11
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12 BP = 2;
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13 if(m < 2*BP)
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14 error('Operator requires at least %d grid points', 2*BP);
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15 end
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16
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17 % Norm
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18 Hv = ones(m,1);
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19 Hv(1) = 1/2;
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20 Hv(m) = 1/2;
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21 Hv = h*Hv;
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22 H = spdiag(Hv, 0);
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23 HI = spdiag(1./Hv, 0);
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24
313
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25 % Boundary operators
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26 e_l = sparse(m,1);
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27 e_l(1) = 1;
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28 e_r = rot90(e_l, 2);
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29
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30 d1_l = sparse(m,1);
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31 d1_l(1:3) = 1/h*[-3/2 2 -1/2];
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32 d1_r = -rot90(d1_l, 2);
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33
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34 d2_l = sparse(m,1);
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35 d2_l(1:3) = 1/h^2*[1 -2 1];
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36 d2_r = rot90(d2_l, 2);
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37
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38 d3_l = sparse(m,1);
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39 d3_l(1:4) = 1/h^3*[-1 3 -3 1];
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40 d3_r = -rot90(d3_l, 2);
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41
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42
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43 % First derivative SBP operator, 1st order accurate at first 6 boundary points
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44 stencil = [-1/2, 0, 1/2];
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45 diags = [-1 0 1];
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46 Q = stripeMatrix(stencil, diags, m);
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47
314
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48 D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r');
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49
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50 % Second derivative, 1st order accurate at first boundary points
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51 M = sparse(m,m);
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52
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53 scheme_width = 3;
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54 scheme_radius = (scheme_width-1)/2;
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55 r = (1+scheme_radius):(m-scheme_radius);
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56
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57 function D2 = D2_fun(c)
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58 Mm1 = -c(r-1)/2 - c(r)/2;
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59 M0 = c(r-1)/2 + c(r) + c(r+1)/2;
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60 Mp1 = -c(r)/2 - c(r+1)/2;
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61
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62 M(r,:) = spdiags([Mm1 M0 Mp1],0:2*scheme_radius,length(r),m);
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64 M(1:2,1:2) = [c(1)/2 + c(2)/2 -c(1)/2 - c(2)/2; -c(1)/2 - c(2)/2 c(1)/2 + c(2) + c(3)/2;];
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65 M(m-1:m,m-1:m) = [c(m-2)/2 + c(m-1) + c(m)/2 -c(m-1)/2 - c(m)/2; -c(m-1)/2 - c(m)/2 c(m-1)/2 + c(m)/2;];
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66 M = 1/h*M;
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67
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68 D2 = HI*(-M - c(1)*e_l*d1_l' + c(m)*e_r*d1_r');
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69 end
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70 D2 = @D2_fun;
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71
313
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72 % Fourth derivative, 0th order accurate at first 6 boundary points
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73 stencil = [1, -4, 6, -4, 1];
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74 diags = -2:2;
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75 M4 = stripeMatrix(stencil, diags, m);
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77 M4_U = [
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78 0.13e2/0.10e2 -0.12e2/0.5e1 0.9e1/0.10e2 0.1e1/0.5e1;
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79 -0.12e2/0.5e1 0.26e2/0.5e1 -0.16e2/0.5e1 0.2e1/0.5e1;
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80 0.9e1/0.10e2 -0.16e2/0.5e1 0.47e2/0.10e2 -0.17e2/0.5e1;
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81 0.1e1/0.5e1 0.2e1/0.5e1 -0.17e2/0.5e1 0.29e2/0.5e1;
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82 ];
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83
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84 M4(1:4,1:4) = M4_U;
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85 M4(m-3:m,m-3:m) = rot90(M4_U, 2);
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86 M4 = 1/h^3*M4;
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87
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88 D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r');
261
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89 end