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view +sbp/+implementations/d4_lonely_6_min_boundary_points.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 b19e142fcae1
children
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function [H, HI, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = d4_variable_6_min_boundary_points(m,h)
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%% 6:te ordn. SBP Finita differens         %%%
    %%% operatorer med diagonal norm            %%%
    %%% Extension to variable koeff             %%%
    %%%                                         %%%
    %%% H           (Normen)                    %%%
    %%% D1=H^(-1)Q  (approx f?rsta derivatan)   %%%
    %%% D2          (approx andra derivatan)    %%%
    %%% D2=HI*(R+C*D*S                          %%%
    %%%                                         %%%
    %%% R=-D1'*H*C*D1-RR                        %%%
    %%%                                         %%%
    %%% RR ?r dissipation)                      %%%
    %%% Dissipationen uppbyggd av D4:           %%%
    %%% DI=D4*B*H*D4                            %%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % H?r med 6 RP ist?llet f?r 8 f?r D4 operatorn, dock samma randderivator

    BP = 6;
    if(m<2*BP)
        error(['Operator requires at least ' num2str(2*BP) ' grid points']);
    end

    % Norm
    Hv = ones(m,1);
    Hv(1:6) = [13649/43200,12013/8640,2711/4320,5359/4320,7877/8640, 43801/43200];
    Hv(m-5:m) = rot90(Hv(1:6),2);
    Hv = h*Hv;
    H = spdiag(Hv, 0);
    HI = spdiag(1./Hv, 0);


    % Boundary operators
    e_l = sparse(m,1);
    e_l(1) = 1;
    e_r = rot90(e_l, 2);

    d1_l = sparse(m,1);
    d1_l(1:5) = [-25/12, 4, -3, 4/3, -1/4]/h;
    d1_r = -rot90(d1_l, 2);

    d2_l = sparse(m,1);
    d2_l(1:5) = [0.35e2/0.12e2 -0.26e2/0.3e1 0.19e2/0.2e1 -0.14e2/0.3e1 0.11e2/0.12e2;]/h^2;
    d2_r = rot90(d2_l, 2);

    d3_l = sparse(m,1);
    d3_l(1:5) = [-0.5e1/0.2e1 9 -12 7 -0.3e1/0.2e1;]/h^3;
    d3_r = -rot90(d3_l, 2);


    % Fourth derivative, 1th order accurate at first 8 boundary points (still
    % yield 5th order convergence if stable: for example u_tt=-u_xxxx

    stencil = [7/240, -2/5, 169/60, -122/15, 91/8, -122/15, 169/60, -2/5, 7/240];
    diags = -4:4;
    M4 = stripeMatrix(stencil, diags, m);

    M4_U=[
        0.3504379e7/0.907200e6 -0.4613983e7/0.453600e6 0.4260437e7/0.453600e6 -0.418577e6/0.113400e6 0.524579e6/0.907200e6 0.535e3/0.18144e5;
        -0.4613983e7/0.453600e6 0.5186159e7/0.181440e6 -0.81121e5/0.2835e4 0.218845e6/0.18144e5 -0.159169e6/0.90720e5 -0.94669e5/0.907200e6;
        0.4260437e7/0.453600e6 -0.81121e5/0.2835e4 0.147695e6/0.4536e4 -0.384457e6/0.22680e5 0.339653e6/0.90720e5 -0.18233e5/0.113400e6;
        -0.418577e6/0.113400e6 0.218845e6/0.18144e5 -0.384457e6/0.22680e5 0.65207e5/0.4536e4 -0.22762e5/0.2835e4 0.1181753e7/0.453600e6;
        0.524579e6/0.907200e6 -0.159169e6/0.90720e5 0.339653e6/0.90720e5 -0.22762e5/0.2835e4 0.2006171e7/0.181440e6 -0.3647647e7/0.453600e6;
        0.535e3/0.18144e5 -0.94669e5/0.907200e6 -0.18233e5/0.113400e6 0.1181753e7/0.453600e6 -0.3647647e7/0.453600e6 0.10305271e8/0.907200e6;
    ];

    M4(1:6,1:6) = M4_U;
    M4(m-5:m,m-5:m) = rot90(M4_U, 2);
    M4 = 1/h^3*M4;

    D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r');
end