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annotate +sbp/+implementations/d4_lonely_8_higher_boundary_order.m @ 774:66eb4a2bbb72 feature/grids

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Remove default scaling of the system. The scaling doens't seem to help actual solutions. One example that fails in the flexural code. With large timesteps the solutions seems to blow up. One particular example is profilePresentation on the tdb_presentation_figures branch with k = 0.0005
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 18 Jul 2018 15:42:52 -0700
parents bf801c3709be
children
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c0cbffcf6513 Created new operator class for lonely D4 operators. Removed some output parameters of implementations.
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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_8_higher_boundary_order(m,h)
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2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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3 %%% 8:te ordn. SBP Finita differens %%%
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4 %%% operatorer med diagonal norm %%%
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5 %%% %%%
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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 %This is 3rd order accurate at the boundary. Not same norm as D1 operator
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19
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20 BP = 8;
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21 if(m<2*BP)
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22 error(['Operator requires at least ' num2str(2*BP) ' grid points']);
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23 end
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25 % Norm
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26 Hv = ones(m,1);
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27 Hv(1:8) = [0.7488203e7/0.25401600e8, 0.5539027e7/0.3628800e7, 0.308923e6/0.1209600e7, 0.1307491e7/0.725760e6, 0.59407e5/0.145152e6, 0.1548947e7/0.1209600e7, 0.3347963e7/0.3628800e7, 0.25641187e8/0.25401600e8];
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28 Hv(m-7:m) = rot90(Hv(1:8),2);
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29 Hv = h*Hv;
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30 H = spdiag(Hv, 0);
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31 HI = spdiag(1./Hv, 0);
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34 % Boundary operators
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35 e_l = sparse(m,1);
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36 e_l(1) = 1;
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37 e_r = rot90(e_l, 2);
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38
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39 d1_l = sparse(m,1);
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40 d1_l(1:7) = [-0.49e2/0.20e2 6 -0.15e2/0.2e1 0.20e2/0.3e1 -0.15e2/0.4e1 0.6e1/0.5e1 -0.1e1/0.6e1]/h;
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41 d1_r = -rot90(d1_l, 2);
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43 d2_l = sparse(m,1);
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44 d2_l(1:7) = [0.203e3/0.45e2 -0.87e2/0.5e1 0.117e3/0.4e1 -0.254e3/0.9e1 0.33e2/0.2e1 -0.27e2/0.5e1 0.137e3/0.180e3]/h^2;
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45 d2_r = rot90(d2_l, 2);
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46
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47 d3_l = sparse(m,1);
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48 d3_l(1:7) = [-0.49e2/0.8e1 29 -0.461e3/0.8e1 62 -0.307e3/0.8e1 13 -0.15e2/0.8e1]/h^3;
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49 d3_r = -rot90(d3_l, 2);
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53 % Fourth derivative, 1th order accurate at first 8 boundary points (still
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54 % yield 5th order convergence if stable: for example u_tt = -u_xxxx
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56 stencil = [-0.41e2/0.7560e4, 0.1261e4/0.15120e5, -0.541e3/0.840e3, 0.4369e4/0.1260e4, -0.1669e4/0.180e3, 0.1529e4/0.120e3, -0.1669e4/0.180e3, 0.4369e4/0.1260e4, -0.541e3/0.840e3, 0.1261e4/0.15120e5,-0.41e2/0.7560e4];
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57 diags = -5:5;
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58 M4 = stripeMatrix(stencil, diags, m);
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60 M4_U = [
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61 0.1031569831e10/0.155675520e9 -0.32874237931e11/0.1452971520e10 0.3069551773e10/0.90810720e8 -0.658395212131e12/0.21794572800e11 0.31068454007e11/0.1816214400e10 -0.39244130657e11/0.7264857600e10 0.1857767503e10/0.2724321600e10 0.1009939e7/0.49420800e8;
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62 -0.32874237931e11/0.1452971520e10 0.12799022387e11/0.155675520e9 -0.134456503627e12/0.1037836800e10 0.15366749479e11/0.129729600e9 -0.207640325549e12/0.3113510400e10 0.5396424073e10/0.259459200e9 -0.858079351e9/0.345945600e9 -0.19806607e8/0.170270100e9;
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63 0.3069551773e10/0.90810720e8 -0.134456503627e12/0.1037836800e10 0.6202056779e10/0.28828800e8 -0.210970327081e12/0.1037836800e10 0.2127730129e10/0.18532800e8 -0.4048692749e10/0.115315200e9 0.1025943959e10/0.259459200e9 0.71054663e8/0.290594304e9;
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64 -0.658395212131e12/0.21794572800e11 0.15366749479e11/0.129729600e9 -0.210970327081e12/0.1037836800e10 0.31025293213e11/0.155675520e9 -0.1147729001e10/0.9884160e7 0.1178067773e10/0.32432400e8 -0.13487255581e11/0.3113510400e10 -0.231082547e9/0.1816214400e10;
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65 0.31068454007e11/0.1816214400e10 -0.207640325549e12/0.3113510400e10 0.2127730129e10/0.18532800e8 -0.1147729001e10/0.9884160e7 0.11524865123e11/0.155675520e9 -0.29754506009e11/0.1037836800e10 0.14231221e8/0.2316600e7 -0.15030629699e11/0.21794572800e11;
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66 -0.39244130657e11/0.7264857600e10 0.5396424073e10/0.259459200e9 -0.4048692749e10/0.115315200e9 0.1178067773e10/0.32432400e8 -0.29754506009e11/0.1037836800e10 0.572247737e9/0.28828800e8 -0.11322059051e11/0.1037836800e10 0.3345834083e10/0.908107200e9;
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67 0.1857767503e10/0.2724321600e10 -0.858079351e9/0.345945600e9 0.1025943959e10/0.259459200e9 -0.13487255581e11/0.3113510400e10 0.14231221e8/0.2316600e7 -0.11322059051e11/0.1037836800e10 0.10478882597e11/0.778377600e9 -0.68446325191e11/0.7264857600e10;
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68 0.1009939e7/0.49420800e8 -0.19806607e8/0.170270100e9 0.71054663e8/0.290594304e9 -0.231082547e9/0.1816214400e10 -0.15030629699e11/0.21794572800e11 0.3345834083e10/0.908107200e9 -0.68446325191e11/0.7264857600e10 0.9944747557e10/0.778377600e9;
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69 ];
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71 M4(1:8,1:8) = M4_U;
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72 M4(m-7:m,m-7: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