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annotate +sbp/+implementations/d4_lonely_4_min_boundary_points.m @ 1337:bf2554f1825d feature/D2_boundary_opt

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Add periodic D1 and D2 operators for orders 8,10,12
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Fri, 13 May 2022 13:28:10 +0200
parents b19e142fcae1
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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c0cbffcf6513 Created new operator class for lonely D4 operators. Removed some output parameters of implementations.
Jonatan Werpers <jonatan@werpers.com>
parents: 318
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1 function [H, HI, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = d4_variable_4_min_boundary_points(m,h)
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parents: 310
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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3 %%% 4:de ordn. SBP Finita differens %%%
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4 %%% operatorer framtagna av Mark Carpenter %%%
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5 %%% %%%
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6 %%% H (Normen) %%%
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7 %%% D1=H^(-1)Q (approx f?rsta derivatan) %%%
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8 %%% D2 (approx andra derivatan) %%%
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9 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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10 %H?r med endast 4 randpunkter
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249
02423f9323c6 Started modifying operator files.
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12
318
99005a80b4c2 Cleaned up d4_variable_4_min_boundary. Removed incorrect D2s from a bunch of files.
Jonatan Werpers <jonatan@werpers.com>
parents: 312
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13 BP = 4;
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parents: 312
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14 if(m<2*BP)
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parents: 312
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15 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
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parents: 312
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16 end
99005a80b4c2 Cleaned up d4_variable_4_min_boundary. Removed incorrect D2s from a bunch of files.
Jonatan Werpers <jonatan@werpers.com>
parents: 312
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17
99005a80b4c2 Cleaned up d4_variable_4_min_boundary. Removed incorrect D2s from a bunch of files.
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parents: 312
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18
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parents: 312
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19 % Norm
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Jonatan Werpers <jonatan@werpers.com>
parents: 312
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20 Hv = ones(m,1);
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21 Hv(1:4) = [17/48 59/48 43/48 49/48];
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22 Hv(m-3:m) = rot90(Hv(1:4),2);
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parents: 312
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23 Hv = h*Hv;
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parents: 312
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24 H = spdiag(Hv, 0);
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25 HI = spdiag(1./Hv, 0);
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26
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27
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28 % Boundary operators
318
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parents: 312
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29 e_l = sparse(m,1);
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parents: 312
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30 e_l(1) = 1;
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31 e_r = rot90(e_l, 2);
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32
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33 d1_l = sparse(m,1);
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parents: 312
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34 d1_l(1:4) = 1/h*[-11/6 3 -3/2 1/3];
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35 d1_r = -rot90(d1_l, 2);
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36
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37 d2_l = sparse(m,1);
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parents: 312
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38 d2_l(1:4) = 1/h^2*[2 -5 4 -1];
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parents: 312
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39 d2_r = rot90(d2_l, 2);
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parents: 312
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41 d3_l = sparse(m,1);
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parents: 312
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42 d3_l(1:4) = 1/h^3*[-1 3 -3 1];
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parents: 312
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43 d3_r = -rot90(d3_l, 2);
249
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44
246
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318
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parents: 312
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46 % First derivative
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parents: 312
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47 stencil = [1/12 -2/3 0 2/3 -1/12];
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48 diags = [-1 0 1];
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49
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50 Q_U = [
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51 0 0.59e2/0.96e2 -0.1e1/0.12e2 -0.1e1/0.32e2;
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52 -0.59e2/0.96e2 0 0.59e2/0.96e2 0;
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53 0.1e1/0.12e2 -0.59e2/0.96e2 0 0.59e2/0.96e2;
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54 0.1e1/0.32e2 0 -0.59e2/0.96e2 0;
249
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55 ];
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56
318
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parents: 312
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57 Q = stripeMatrix(stencil, diags, m);
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parents: 312
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58 Q(1:4,1:4)=Q_U;
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parents: 312
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59 Q(m-3:m,m-3:m) = -rot90(Q_U, 2);
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61 D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r');
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318
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parents: 312
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63 % Fourth derivative
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parents: 312
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64 stencil = [-1/6, 2, -13/2, 28/3, -13/2, 2, -1/6];
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parents: 312
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65 diags = -3:3;
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66 M4 = stripeMatrix(stencil, diags, m);
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67
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68 M4_U=[
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69 0.8e1/0.3e1 -0.37e2/0.6e1 0.13e2/0.3e1 -0.5e1/0.6e1;
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70 -0.37e2/0.6e1 0.47e2/0.3e1 -13 0.11e2/0.3e1;
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71 0.13e2/0.3e1 -13 0.44e2/0.3e1 -0.47e2/0.6e1;
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72 -0.5e1/0.6e1 0.11e2/0.3e1 -0.47e2/0.6e1 0.29e2/0.3e1;
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73 ];
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74
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76 M4(1:4,1:4) = M4_U;
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parents: 312
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77 M4(m-3:m,m-3:m) = rot90(M4_U, 2);
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parents: 312
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78 M4 = 1/h^3*M4;
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79
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80 D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r');
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81 end