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view +sbp/+implementations/d2_variable_periodic_6.m @ 1037:2d7ba44340d0 feature/burgers1d
Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
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date | Fri, 18 Jan 2019 09:02:02 +0100 |
parents | bbf303c1f0cf |
children |
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function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_6(m,h) % m = number of unique grid points, i.e. h = L/m; if(m<7) error(['Operator requires at least ' num2str(7) ' grid points']); end % Norm Hv = ones(m,1); Hv = h*Hv; H = spdiag(Hv, 0); HI = spdiag(1./Hv, 0); % Dummy boundary operators e_l = sparse(m,1); e_r = rot90(e_l, 2); d1_l = sparse(m,1); d1_r = -rot90(d1_l, 2); % D1 operator diags = -3:3; stencil = [-1/60 9/60 -45/60 0 45/60 -9/60 1/60]; D1 = stripeMatrixPeriodic(stencil, diags, m); D1 = D1/h; % D2 operator scheme_width = 7; scheme_radius = (scheme_width-1)/2; r = 1:m; offset = scheme_width; r = r + offset; function D2 = D2_fun(c) c = [c(end-scheme_width+1:end); c; c(1:scheme_width) ]; Mm3 = c(r-2)/0.40e2 + c(r-1)/0.40e2 - 0.11e2/0.360e3 * c(r-3) - 0.11e2/0.360e3 * c(r); Mm2 = c(r-3)/0.20e2 - 0.3e1/0.10e2 * c(r-1) + c(r+1)/0.20e2 + 0.7e1/0.40e2 * c(r) + 0.7e1/0.40e2 * c(r-2); Mm1 = -c(r-3)/0.40e2 - 0.3e1/0.10e2 * c(r-2) - 0.3e1/0.10e2 * c(r+1) - c(r+2)/0.40e2 - 0.17e2/0.40e2 * c(r) - 0.17e2/0.40e2 * c(r-1); M0 = c(r-3)/0.180e3 + c(r-2)/0.8e1 + 0.19e2/0.20e2 * c(r-1) + 0.19e2/0.20e2 * c(r+1) + c(r+2)/0.8e1 + c(r+3)/0.180e3 + 0.101e3/0.180e3 * c(r); Mp1 = -c(r-2)/0.40e2 - 0.3e1/0.10e2 * c(r-1) - 0.3e1/0.10e2 * c(r+2) - c(r+3)/0.40e2 - 0.17e2/0.40e2 * c(r) - 0.17e2/0.40e2 * c(r+1); Mp2 = c(r-1)/0.20e2 - 0.3e1/0.10e2 * c(r+1) + c(r+3)/0.20e2 + 0.7e1/0.40e2 * c(r) + 0.7e1/0.40e2 * c(r+2); Mp3 = c(r+1)/0.40e2 + c(r+2)/0.40e2 - 0.11e2/0.360e3 * c(r) - 0.11e2/0.360e3 * c(r+3); vals = [Mm3,Mm2,Mm1,M0,Mp1,Mp2,Mp3]; diags = -scheme_radius : scheme_radius; M = spdiagsPeriodic(vals,diags); M=M/h; D2=HI*(-M ); end D2 = @D2_fun; end