Mercurial > repos > public > sbplib
view diracDiscr.m @ 652:be941bb0a11a feature/d1_staggered
Add staggered 1D variable coefficient. Convergence study working.
author | Martin Almquist <malmquist@stanford.edu> |
---|---|
date | Mon, 04 Dec 2017 11:11:03 -0800 |
parents | 4ee7d15bd8e6 |
children | 5264ce57b573 |
line wrap: on
line source
function ret = diracDiscr(x_0in , x , m_order, s_order, H) m = length(x); % Return zeros if x0 is outside grid if(x_0in < x(1) || x_0in > x(end) ) ret = zeros(size(x)); else fnorm = diag(H); eta = abs(x-x_0in); h = x(2)-x(1); tot = m_order+s_order; S = []; M = []; poss = find(tot*h/2 >= eta); % Ensure that poss is not too long if length(poss) == (tot + 2) poss = poss(2:end-1); elseif length(poss) == (tot + 1) poss = poss(1:end-1); end % Use first tot grid points if length(poss)<tot && x_0in < x(1) + ceil(tot/2)*h; index=1:tot; pol=(x(1:tot)-x(1))/(x(tot)-x(1)); x_0=(x_0in-x(1))/(x(tot)-x(1)); norm=fnorm(1:tot)/h; % Use last tot grid points elseif length(poss)<tot && x_0in > x(end) - ceil(tot/2)*h; index = length(x)-tot+1:length(x); pol = (x(end-tot+1:end)-x(end-tot+1))/(x(end)-x(end-tot+1)); norm = fnorm(end-tot+1:end)/h; x_0 = (x_0in-x(end-tot+1))/(x(end)-x(end-tot+1)); % Interior, compensate for round-off errors. elseif length(poss) < tot if poss(end)<m poss = [poss; poss(end)+1]; else poss = [poss(1)-1; poss]; end pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1))); x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1))); norm = fnorm(poss)/h; index = poss; % Interior else pol = (x(poss)-x(poss(1)))/(x(poss(end))-x(poss(1))); x_0 = (x_0in-x(poss(1)))/(x(poss(end))-x(poss(1))); norm = fnorm(poss)/h; index = poss; end h_pol = pol(2)-pol(1); b = zeros(m_order+s_order,1); for i = 1:m_order b(i,1) = x_0^(i-1); end for i = 1:(m_order+s_order) for j = 1:m_order M(j,i) = pol(i)^(j-1)*h_pol*norm(i); end end for i = 1:(m_order+s_order) for j = 1:s_order S(j,i) = (-1)^(i-1)*pol(i)^(j-1); end end A = [M;S]; d = A\b; ret = x*0; ret(index) = d/h*h_pol; end end