Mercurial > repos > public > sbplib
diff +sbp/+implementations/d1_noneq_minimal_6.m @ 261:6009f2712d13 operator_remake
Moved and renamned all implementations.
author | Martin Almquist <martin.almquist@it.uu.se> |
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date | Thu, 08 Sep 2016 15:35:45 +0200 |
parents | |
children | bfa130b7abf6 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+sbp/+implementations/d1_noneq_minimal_6.m Thu Sep 08 15:35:45 2016 +0200 @@ -0,0 +1,128 @@ +function [D1,H,x,h] = d1_noneq_minimal_6(N,L) + +% L: Domain length +% N: Number of grid points +if(nargin < 2) + L = 1; +end + +% BP: Number of boundary points +% m: Number of nonequidistant spacings +% order: Accuracy of interior stencil +BP = 5; +m = 2; +order = 6; + +%%%% Non-equidistant grid points %%%%% +x0 = 0.0000000000000e+00; +x1 = 4.0842950991998e-01; +x2 = 1.1968523189207e+00; +x3 = 2.1968523189207e+00; +x4 = 3.1968523189207e+00; +x5 = 4.1968523189207e+00; + +xb = zeros(m+1,1); +for i = 0:m + xb(i+1) = eval(['x' num2str(i)]); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%% Compute h %%%%%%%%%% +h = L/(2*xb(end) + N-1-2*m); +%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%% Define grid %%%%%%%% +x = h*[xb; linspace(xb(end)+1,L/h-xb(end)-1,N-2*(m+1))'; L/h-flip(xb) ]; +%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%% Norm matrix %%%%%%%% +P = zeros(BP,1); +%#ok<*NASGU> +P0 = 1.2740260779883e-01; +P1 = 6.1820981002054e-01; +P2 = 9.4308973897679e-01; +P3 = 1.0093019060199e+00; +P4 = 9.9884825610465e-01; + +for i = 0:BP-1 + P(i+1) = eval(['P' num2str(i)]); +end + +H = ones(N,1); +H(1:BP) = P; +H(end-BP+1:end) = flip(P); +H = spdiags(h*H,0,N,N); +%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%% Q matrix %%%%%%%%%%% + +% interior stencil +switch order + case 2 + d = [-1/2,0,1/2]; + case 4 + d = [1/12,-2/3,0,2/3,-1/12]; + case 6 + d = [-1/60,3/20,-3/4,0,3/4,-3/20,1/60]; + case 8 + d = [1/280,-4/105,1/5,-4/5,0,4/5,-1/5,4/105,-1/280]; + case 10 + d = [-1/1260,5/504,-5/84,5/21,-5/6,0,5/6,-5/21,5/84,-5/504,1/1260]; + case 12 + d = [1/5544,-1/385,1/56,-5/63,15/56,-6/7,0,6/7,-15/56,5/63,-1/56,1/385,-1/5544]; +end +d = repmat(d,N,1); +Q = spdiags(d,-order/2:order/2,N,N); + +% Boundaries +Q0_0 = -5.0000000000000e-01; +Q0_1 = 6.3217364546846e-01; +Q0_2 = -1.6411963429825e-01; +Q0_3 = 3.6495407984639e-02; +Q0_4 = -4.5494191548490e-03; +Q0_5 = 0.0000000000000e+00; +Q0_6 = 0.0000000000000e+00; +Q0_7 = 0.0000000000000e+00; +Q1_0 = -6.3217364546846e-01; +Q1_1 = 0.0000000000000e+00; +Q1_2 = 8.0515625504417e-01; +Q1_3 = -2.0755653563249e-01; +Q1_4 = 3.4573926056780e-02; +Q1_5 = 0.0000000000000e+00; +Q1_6 = 0.0000000000000e+00; +Q1_7 = 0.0000000000000e+00; +Q2_0 = 1.6411963429825e-01; +Q2_1 = -8.0515625504417e-01; +Q2_2 = 0.0000000000000e+00; +Q2_3 = 7.9402676057785e-01; +Q2_4 = -1.6965680649860e-01; +Q2_5 = 1.6666666666667e-02; +Q2_6 = 0.0000000000000e+00; +Q2_7 = 0.0000000000000e+00; +Q3_0 = -3.6495407984639e-02; +Q3_1 = 2.0755653563249e-01; +Q3_2 = -7.9402676057785e-01; +Q3_3 = 0.0000000000000e+00; +Q3_4 = 7.5629896626333e-01; +Q3_5 = -1.5000000000000e-01; +Q3_6 = 1.6666666666667e-02; +Q3_7 = 0.0000000000000e+00; +Q4_0 = 4.5494191548490e-03; +Q4_1 = -3.4573926056780e-02; +Q4_2 = 1.6965680649860e-01; +Q4_3 = -7.5629896626333e-01; +Q4_4 = 0.0000000000000e+00; +Q4_5 = 7.5000000000000e-01; +Q4_6 = -1.5000000000000e-01; +Q4_7 = 1.6666666666667e-02; +for i = 1:BP + for j = 1:BP + Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]); + Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]); + end +end +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%% Difference operator %% +D1 = H\Q; +%%%%%%%%%%%%%%%%%%%%%%%%%%% \ No newline at end of file