Mercurial > repos > public > sbplib
diff +sbp/+implementations/d1_noneq_minimal_8.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_8.m Thu Sep 08 15:35:45 2016 +0200 @@ -0,0 +1,150 @@ +function [D1,H,x,h] = d1_noneq_minimal_8(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 = 6; +m = 2; +order = 8; + +%%%% Non-equidistant grid points %%%%% +x0 = 0.0000000000000e+00; +x1 = 4.9439570885261e-01; +x2 = 1.4051531374839e+00; +x3 = 2.4051531374839e+00; +x4 = 3.4051531374839e+00; +x5 = 4.4051531374839e+00; +x6 = 5.4051531374839e+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 = 1.4523997892351e-01; +P1 = 7.6864793350174e-01; +P2 = 9.9116487068535e-01; +P3 = 9.9992473335107e-01; +P4 = 1.0002097054636e+00; +P5 = 9.9996591555866e-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 = 6.6697342753834e-01; +Q0_2 = -2.2919342278749e-01; +Q0_3 = 7.4283116457276e-02; +Q0_4 = -1.2020661178873e-02; +Q0_5 = -4.2460029252999e-05; +Q0_6 = 0.0000000000000e+00; +Q0_7 = 0.0000000000000e+00; +Q0_8 = 0.0000000000000e+00; +Q0_9 = 0.0000000000000e+00; +Q1_0 = -6.6697342753834e-01; +Q1_1 = 0.0000000000000e+00; +Q1_2 = 8.8241196934163e-01; +Q1_3 = -2.6653314104602e-01; +Q1_4 = 5.5302527504316e-02; +Q1_5 = -4.2079282615860e-03; +Q1_6 = 0.0000000000000e+00; +Q1_7 = 0.0000000000000e+00; +Q1_8 = 0.0000000000000e+00; +Q1_9 = 0.0000000000000e+00; +Q2_0 = 2.2919342278749e-01; +Q2_1 = -8.8241196934163e-01; +Q2_2 = 0.0000000000000e+00; +Q2_3 = 8.2904844081126e-01; +Q2_4 = -2.1156614214635e-01; +Q2_5 = 3.9307676460659e-02; +Q2_6 = -3.5714285714286e-03; +Q2_7 = 0.0000000000000e+00; +Q2_8 = 0.0000000000000e+00; +Q2_9 = 0.0000000000000e+00; +Q3_0 = -7.4283116457276e-02; +Q3_1 = 2.6653314104602e-01; +Q3_2 = -8.2904844081126e-01; +Q3_3 = 0.0000000000000e+00; +Q3_4 = 8.0305501223679e-01; +Q3_5 = -2.0078040553808e-01; +Q3_6 = 3.8095238095238e-02; +Q3_7 = -3.5714285714286e-03; +Q3_8 = 0.0000000000000e+00; +Q3_9 = 0.0000000000000e+00; +Q4_0 = 1.2020661178873e-02; +Q4_1 = -5.5302527504316e-02; +Q4_2 = 2.1156614214635e-01; +Q4_3 = -8.0305501223679e-01; +Q4_4 = 0.0000000000000e+00; +Q4_5 = 8.0024692689207e-01; +Q4_6 = -2.0000000000000e-01; +Q4_7 = 3.8095238095238e-02; +Q4_8 = -3.5714285714286e-03; +Q4_9 = 0.0000000000000e+00; +Q5_0 = 4.2460029252999e-05; +Q5_1 = 4.2079282615860e-03; +Q5_2 = -3.9307676460659e-02; +Q5_3 = 2.0078040553808e-01; +Q5_4 = -8.0024692689207e-01; +Q5_5 = 0.0000000000000e+00; +Q5_6 = 8.0000000000000e-01; +Q5_7 = -2.0000000000000e-01; +Q5_8 = 3.8095238095238e-02; +Q5_9 = -3.5714285714286e-03; +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