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annotate +sbp/+implementations/d4_variable_6_2.m @ 321:5c9e5ba1c1ab feature/beams

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Clean up of d4_variable_6_2.m
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 26 Sep 2016 09:04:57 +0200
parents 99005a80b4c2
children c0cbffcf6513
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1 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_6_2(m,h)
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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3 %%% 6:te ordn. SBP Finita differens %%%
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4 %%% operatorer med diagonal norm %%%
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5 %%% Extension to variable koeff %%%
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6 %%% %%%
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7 %%% H (Normen) %%%
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8 %%% D1=H^(-1)Q (approx f?rsta derivatan) %%%
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9 %%% D2 (approx andra derivatan) %%%
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10 %%% D2=HI*(R+C*D*S %%%
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11 %%% %%%
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12 %%% R=-D1'*H*C*D1-RR %%%
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13 %%% %%%
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14 %%% RR ?r dissipation) %%%
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15 %%% Dissipationen uppbyggd av D4: %%%
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16 %%% DI=D4*B*H*D4 %%%
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17 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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18
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19 % H?r med 6 RP ist?llet f?r 8 f?r D4 operatorn, dock samma randderivator
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20 % Denna ?r noggrannare, och har 2a ordningens randdslutning och b?r ge 6te
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21 % ordningens konvergens. Hade dock ingen fri parameter att optimera
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22
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23 BP = 6;
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24 if(m<2*BP)
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25 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
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26 end
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28 % Norm
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29 Hv = ones(m,1);
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30 Hv(1:6) = [0.181e3/0.576e3, 0.1343e4/0.960e3, 0.293e3/0.480e3, 0.1811e4/0.1440e4, 0.289e3/0.320e3, 0.65e2/0.64e2];
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31 Hv(m-5:m) = rot90(Hv(1:6),2);
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32 Hv = h*Hv;
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33 H = spdiag(Hv, 0);
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34 HI = spdiag(1./Hv, 0);
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37 % Boundary operators
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38 e_l = sparse(m,1);
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39 e_l(1) = 1;
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40 e_r = rot90(e_l, 2);
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42 d1_l = sparse(m,1);
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43 d1_l(1:6) = [-0.137e3/0.60e2 5 -5 0.10e2/0.3e1 -0.5e1/0.4e1 0.1e1/0.5e1;]/h;
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44 d1_r = -rot90(d1_l);
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46 d2_l = sparse(m,1);
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47 d2_l(1:6) = [0.15e2/0.4e1 -0.77e2/0.6e1 0.107e3/0.6e1 -13 0.61e2/0.12e2 -0.5e1/0.6e1;]/h^2;
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48 d2_r = rot90(d2_l, 2);
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50 d3_l = sparse(m,1);
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51 d3_l(1:6) = [-0.17e2/0.4e1 0.71e2/0.4e1 -0.59e2/0.2e1 0.49e2/0.2e1 -0.41e2/0.4e1 0.7e1/0.4e1;]/h^3;
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52 d3_r = -rot90(d3_l, 2);
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55 % Fourth derivative, 1th order accurate at first 8 boundary points (still
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56 % yield 5th order convergence if stable: for example u_tt = -u_xxxx
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57 stencil = [7/240, -2/5, 169/60, -122/15, 91/8, -122/15, 169/60, -2/5, 7/240];
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58 diags = -4:4;
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59 M4 = stripeMatrix(stencil, diags, m);
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61 M4_U = [
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62 0.1009e4/0.192e3 -0.7657e4/0.480e3 0.9307e4/0.480e3 -0.509e3/0.40e2 0.4621e4/0.960e3 -0.25e2/0.32e2;
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63 -0.7657e4/0.480e3 0.49513e5/0.960e3 -0.4007e4/0.60e2 0.21799e5/0.480e3 -0.8171e4/0.480e3 0.2657e4/0.960e3;
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64 0.9307e4/0.480e3 -0.4007e4/0.60e2 0.1399e4/0.15e2 -0.2721e4/0.40e2 0.12703e5/0.480e3 -0.521e3/0.120e3;
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65 -0.509e3/0.40e2 0.21799e5/0.480e3 -0.2721e4/0.40e2 0.3349e4/0.60e2 -0.389e3/0.15e2 0.559e3/0.96e2;
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66 0.4621e4/0.960e3 -0.8171e4/0.480e3 0.12703e5/0.480e3 -0.389e3/0.15e2 0.17857e5/0.960e3 -0.1499e4/0.160e3;
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67 -0.25e2/0.32e2 0.2657e4/0.960e3 -0.521e3/0.120e3 0.559e3/0.96e2 -0.1499e4/0.160e3 0.2225e4/0.192e3;
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68 ];
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71 M4(1:6,1:6) = M4_U;
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72 M4(m-5:m,m-5:m) = rot90(M4_U, 2);
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73 M4 = 1/h^3*M4;
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74
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75 D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r');
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76 end