Mercurial > repos > public > sbplib
diff +sbp/+implementations/d1_noneq_10.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_10.m Thu Sep 08 15:35:45 2016 +0200 @@ -0,0 +1,248 @@ +function [D1,H,x,h] = d1_noneq_10(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 = 10; +m = 5; +order = 10; + +%%%% Non-equidistant grid points %%%%% +x0 = 0.0000000000000e+00; +x1 = 3.5902433622052e-01; +x2 = 1.1436659188355e+00; +x3 = 2.2144895894456e+00; +x4 = 3.3682742337736e+00; +x5 = 4.4309689056870e+00; +x6 = 5.4309689056870e+00; +x7 = 6.4309689056870e+00; +x8 = 7.4309689056870e+00; +x9 = 8.4309689056870e+00; +x10 = 9.4309689056870e+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 = 1.0000000000000e-01; +P1 = 5.8980851260667e-01; +P2 = 9.5666820955973e-01; +P3 = 1.1500297411596e+00; +P4 = 1.1232986993248e+00; +P5 = 1.0123020150951e+00; +P6 = 9.9877122702527e-01; +P7 = 1.0000873322761e+00; +P8 = 1.0000045540888e+00; +P9 = 9.9999861455083e-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 = 6.7548747038002e-01; +Q0_2 = -2.6691978151546e-01; +Q0_3 = 1.4438714982130e-01; +Q0_4 = -7.7273673750760e-02; +Q0_5 = 2.5570078343005e-02; +Q0_6 = 4.2808774693299e-03; +Q0_7 = -8.2902108933389e-03; +Q0_8 = 3.2031176427908e-03; +Q0_9 = -4.4502749689556e-04; +Q0_10 = 0.0000000000000e+00; +Q0_11 = 0.0000000000000e+00; +Q0_12 = 0.0000000000000e+00; +Q0_13 = 0.0000000000000e+00; +Q0_14 = 0.0000000000000e+00; +Q1_0 = -6.7548747038002e-01; +Q1_1 = 0.0000000000000e+00; +Q1_2 = 9.5146052715180e-01; +Q1_3 = -4.2442349882626e-01; +Q1_4 = 2.1538865145190e-01; +Q1_5 = -7.1939778160350e-02; +Q1_6 = -8.2539187832840e-03; +Q1_7 = 1.9930661669090e-02; +Q1_8 = -7.7433256989613e-03; +Q1_9 = 1.0681515760869e-03; +Q1_10 = 0.0000000000000e+00; +Q1_11 = 0.0000000000000e+00; +Q1_12 = 0.0000000000000e+00; +Q1_13 = 0.0000000000000e+00; +Q1_14 = 0.0000000000000e+00; +Q2_0 = 2.6691978151546e-01; +Q2_1 = -9.5146052715180e-01; +Q2_2 = 0.0000000000000e+00; +Q2_3 = 9.6073770842387e-01; +Q2_4 = -3.9378595264609e-01; +Q2_5 = 1.3302097358959e-01; +Q2_6 = 8.1200458151489e-05; +Q2_7 = -2.3849770528789e-02; +Q2_8 = 9.6600442856829e-03; +Q2_9 = -1.3234579460680e-03; +Q2_10 = 0.0000000000000e+00; +Q2_11 = 0.0000000000000e+00; +Q2_12 = 0.0000000000000e+00; +Q2_13 = 0.0000000000000e+00; +Q2_14 = 0.0000000000000e+00; +Q3_0 = -1.4438714982130e-01; +Q3_1 = 4.2442349882626e-01; +Q3_2 = -9.6073770842387e-01; +Q3_3 = 0.0000000000000e+00; +Q3_4 = 9.1551097634196e-01; +Q3_5 = -2.8541713079648e-01; +Q3_6 = 4.1398809121293e-02; +Q3_7 = 1.7256059167927e-02; +Q3_8 = -9.4349194803610e-03; +Q3_9 = 1.3875650645663e-03; +Q3_10 = 0.0000000000000e+00; +Q3_11 = 0.0000000000000e+00; +Q3_12 = 0.0000000000000e+00; +Q3_13 = 0.0000000000000e+00; +Q3_14 = 0.0000000000000e+00; +Q4_0 = 7.7273673750760e-02; +Q4_1 = -2.1538865145190e-01; +Q4_2 = 3.9378595264609e-01; +Q4_3 = -9.1551097634196e-01; +Q4_4 = 0.0000000000000e+00; +Q4_5 = 8.3519401865051e-01; +Q4_6 = -2.0586492924974e-01; +Q4_7 = 3.1230261235901e-02; +Q4_8 = -2.0969453466651e-04; +Q4_9 = -5.0965470499782e-04; +Q4_10 = 0.0000000000000e+00; +Q4_11 = 0.0000000000000e+00; +Q4_12 = 0.0000000000000e+00; +Q4_13 = 0.0000000000000e+00; +Q4_14 = 0.0000000000000e+00; +Q5_0 = -2.5570078343005e-02; +Q5_1 = 7.1939778160350e-02; +Q5_2 = -1.3302097358959e-01; +Q5_3 = 2.8541713079648e-01; +Q5_4 = -8.3519401865051e-01; +Q5_5 = 0.0000000000000e+00; +Q5_6 = 8.1046389580138e-01; +Q5_7 = -2.1879194972141e-01; +Q5_8 = 5.2977237804899e-02; +Q5_9 = -9.0146730522360e-03; +Q5_10 = 7.9365079365079e-04; +Q5_11 = 0.0000000000000e+00; +Q5_12 = 0.0000000000000e+00; +Q5_13 = 0.0000000000000e+00; +Q5_14 = 0.0000000000000e+00; +Q6_0 = -4.2808774693299e-03; +Q6_1 = 8.2539187832840e-03; +Q6_2 = -8.1200458151489e-05; +Q6_3 = -4.1398809121293e-02; +Q6_4 = 2.0586492924974e-01; +Q6_5 = -8.1046389580138e-01; +Q6_6 = 0.0000000000000e+00; +Q6_7 = 8.2787884456005e-01; +Q6_8 = -2.3582460382545e-01; +Q6_9 = 5.9178678209520e-02; +Q6_10 = -9.9206349206349e-03; +Q6_11 = 7.9365079365079e-04; +Q6_12 = 0.0000000000000e+00; +Q6_13 = 0.0000000000000e+00; +Q6_14 = 0.0000000000000e+00; +Q7_0 = 8.2902108933389e-03; +Q7_1 = -1.9930661669090e-02; +Q7_2 = 2.3849770528789e-02; +Q7_3 = -1.7256059167927e-02; +Q7_4 = -3.1230261235901e-02; +Q7_5 = 2.1879194972141e-01; +Q7_6 = -8.2787884456005e-01; +Q7_7 = 0.0000000000000e+00; +Q7_8 = 8.3301028859275e-01; +Q7_9 = -2.3804321850015e-01; +Q7_10 = 5.9523809523809e-02; +Q7_11 = -9.9206349206349e-03; +Q7_12 = 7.9365079365079e-04; +Q7_13 = 0.0000000000000e+00; +Q7_14 = 0.0000000000000e+00; +Q8_0 = -3.2031176427908e-03; +Q8_1 = 7.7433256989613e-03; +Q8_2 = -9.6600442856829e-03; +Q8_3 = 9.4349194803610e-03; +Q8_4 = 2.0969453466651e-04; +Q8_5 = -5.2977237804899e-02; +Q8_6 = 2.3582460382545e-01; +Q8_7 = -8.3301028859275e-01; +Q8_8 = 0.0000000000000e+00; +Q8_9 = 8.3333655748509e-01; +Q8_10 = -2.3809523809524e-01; +Q8_11 = 5.9523809523809e-02; +Q8_12 = -9.9206349206349e-03; +Q8_13 = 7.9365079365079e-04; +Q8_14 = 0.0000000000000e+00; +Q9_0 = 4.4502749689556e-04; +Q9_1 = -1.0681515760869e-03; +Q9_2 = 1.3234579460680e-03; +Q9_3 = -1.3875650645663e-03; +Q9_4 = 5.0965470499782e-04; +Q9_5 = 9.0146730522360e-03; +Q9_6 = -5.9178678209520e-02; +Q9_7 = 2.3804321850015e-01; +Q9_8 = -8.3333655748509e-01; +Q9_9 = 0.0000000000000e+00; +Q9_10 = 8.3333333333333e-01; +Q9_11 = -2.3809523809524e-01; +Q9_12 = 5.9523809523809e-02; +Q9_13 = -9.9206349206349e-03; +Q9_14 = 7.9365079365079e-04; +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