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view +sbp/+implementations/d1_noneq_12.m @ 261:6009f2712d13 operator_remake

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Moved and renamned all implementations.
author Martin Almquist <martin.almquist@it.uu.se>
date Thu, 08 Sep 2016 15:35:45 +0200
parents
children bfa130b7abf6
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function [D1,H,x,h] = d1_noneq_12(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 = 12;
m = 6;
order = 12;

%%%% Non-equidistant grid points %%%%%
x0 =  0.0000000000000e+00;
x1 =  3.6098032343909e-01;
x2 =  1.1634317168086e+00;
x3 =  2.2975905356987e+00;
x4 =  3.6057529790929e+00;
x5 =  4.8918275675510e+00;
x6 =  6.0000000000000e+00;
x7 =  7.0000000000000e+00;
x8 =  8.0000000000000e+00;
x9 =  9.0000000000000e+00;
x10 =  1.0000000000000e+01;
x11 =  1.1000000000000e+01;
x12 =  1.2000000000000e+01;

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 =  1.0000000000011e-01;
P1 =  5.9616216757547e-01;
P2 =  9.9065699844442e-01;
P3 =  1.2512548713913e+00;
P4 =  1.3316678989403e+00;
P5 =  1.2093375037721e+00;
P6 =  1.0236491595704e+00;
P7 =  9.9685258909811e-01;
P8 =  1.0004766563923e+00;
P9 =  9.9993617879146e-01;
P10 =  1.0000063122914e+00;
P11 =  9.9999966373260e-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 =  6.7597560728423e-01;
Q0_2 = -2.6859785384416e-01;
Q0_3 =  1.4850302678903e-01;
Q0_4 = -8.7976689586154e-02;
Q0_5 =  4.1833336322613e-02;
Q0_6 = -2.2216684976993e-03;
Q0_7 = -1.5910034062022e-02;
Q0_8 =  1.1296706376589e-02;
Q0_9 = -3.1823678285130e-03;
Q0_10 =  2.4843594063649e-04;
Q0_11 =  3.1501105449828e-05;
Q0_12 =  0.0000000000000e+00;
Q0_13 =  0.0000000000000e+00;
Q0_14 =  0.0000000000000e+00;
Q0_15 =  0.0000000000000e+00;
Q0_16 =  0.0000000000000e+00;
Q0_17 =  0.0000000000000e+00;
Q1_0 = -6.7597560728423e-01;
Q1_1 =  0.0000000000000e+00;
Q1_2 =  9.5424013647146e-01;
Q1_3 = -4.3389334603464e-01;
Q1_4 =  2.4285669347653e-01;
Q1_5 = -1.1443465137214e-01;
Q1_6 =  8.5942765682435e-03;
Q1_7 =  4.0290424215772e-02;
Q1_8 = -2.9396383714543e-02;
Q1_9 =  8.5601827834256e-03;
Q1_10 = -7.8128092862319e-04;
Q1_11 = -6.0444181254875e-05;
Q1_12 =  0.0000000000000e+00;
Q1_13 =  0.0000000000000e+00;
Q1_14 =  0.0000000000000e+00;
Q1_15 =  0.0000000000000e+00;
Q1_16 =  0.0000000000000e+00;
Q1_17 =  0.0000000000000e+00;
Q2_0 =  2.6859785384416e-01;
Q2_1 = -9.5424013647146e-01;
Q2_2 =  0.0000000000000e+00;
Q2_3 =  9.7065114311923e-01;
Q2_4 = -4.3205328628292e-01;
Q2_5 =  1.9549970932735e-01;
Q2_6 = -2.4406885385172e-02;
Q2_7 = -5.5737279079895e-02;
Q2_8 =  4.3772338637753e-02;
Q2_9 = -1.3727655130726e-02;
Q2_10 =  1.6271304373071e-03;
Q2_11 =  1.7066984372933e-05;
Q2_12 =  0.0000000000000e+00;
Q2_13 =  0.0000000000000e+00;
Q2_14 =  0.0000000000000e+00;
Q2_15 =  0.0000000000000e+00;
Q2_16 =  0.0000000000000e+00;
Q2_17 =  0.0000000000000e+00;
Q3_0 = -1.4850302678903e-01;
Q3_1 =  4.3389334603464e-01;
Q3_2 = -9.7065114311923e-01;
Q3_3 =  0.0000000000000e+00;
Q3_4 =  9.5375878629204e-01;
Q3_5 = -3.6113954384951e-01;
Q3_6 =  6.9749289223875e-02;
Q3_7 =  6.5161366516465e-02;
Q3_8 = -6.0325702283960e-02;
Q3_9 =  2.1188913621662e-02;
Q3_10 = -3.2632650250470e-03;
Q3_11 =  1.3097937809499e-04;
Q3_12 =  0.0000000000000e+00;
Q3_13 =  0.0000000000000e+00;
Q3_14 =  0.0000000000000e+00;
Q3_15 =  0.0000000000000e+00;
Q3_16 =  0.0000000000000e+00;
Q3_17 =  0.0000000000000e+00;
Q4_0 =  8.7976689586154e-02;
Q4_1 = -2.4285669347653e-01;
Q4_2 =  4.3205328628292e-01;
Q4_3 = -9.5375878629204e-01;
Q4_4 =  0.0000000000000e+00;
Q4_5 =  8.8676146394834e-01;
Q4_6 = -2.1292503103800e-01;
Q4_7 = -4.6037018833218e-02;
Q4_8 =  7.4338719466734e-02;
Q4_9 = -3.1217656663809e-02;
Q4_10 =  6.1239492854797e-03;
Q4_11 = -4.5892226603067e-04;
Q4_12 =  0.0000000000000e+00;
Q4_13 =  0.0000000000000e+00;
Q4_14 =  0.0000000000000e+00;
Q4_15 =  0.0000000000000e+00;
Q4_16 =  0.0000000000000e+00;
Q4_17 =  0.0000000000000e+00;
Q5_0 = -4.1833336322613e-02;
Q5_1 =  1.1443465137214e-01;
Q5_2 = -1.9549970932735e-01;
Q5_3 =  3.6113954384951e-01;
Q5_4 = -8.8676146394834e-01;
Q5_5 =  0.0000000000000e+00;
Q5_6 =  7.7461223007026e-01;
Q5_7 = -1.0609547334165e-01;
Q5_8 = -4.4853791547749e-02;
Q5_9 =  3.2436468405486e-02;
Q5_10 = -8.4387621360184e-03;
Q5_11 =  8.5964292632428e-04;
Q5_12 =  0.0000000000000e+00;
Q5_13 =  0.0000000000000e+00;
Q5_14 =  0.0000000000000e+00;
Q5_15 =  0.0000000000000e+00;
Q5_16 =  0.0000000000000e+00;
Q5_17 =  0.0000000000000e+00;
Q6_0 =  2.2216684976993e-03;
Q6_1 = -8.5942765682435e-03;
Q6_2 =  2.4406885385172e-02;
Q6_3 = -6.9749289223875e-02;
Q6_4 =  2.1292503103800e-01;
Q6_5 = -7.7461223007026e-01;
Q6_6 =  0.0000000000000e+00;
Q6_7 =  7.4758103262966e-01;
Q6_8 = -1.5730779067906e-01;
Q6_9 =  2.6517620342970e-02;
Q6_10 = -4.3175367549700e-03;
Q6_11 =  1.1092605832824e-03;
Q6_12 = -1.8037518037522e-04;
Q6_13 =  0.0000000000000e+00;
Q6_14 =  0.0000000000000e+00;
Q6_15 =  0.0000000000000e+00;
Q6_16 =  0.0000000000000e+00;
Q6_17 =  0.0000000000000e+00;
Q7_0 =  1.5910034062022e-02;
Q7_1 = -4.0290424215772e-02;
Q7_2 =  5.5737279079895e-02;
Q7_3 = -6.5161366516465e-02;
Q7_4 =  4.6037018833218e-02;
Q7_5 =  1.0609547334165e-01;
Q7_6 = -7.4758103262966e-01;
Q7_7 =  0.0000000000000e+00;
Q7_8 =  8.0975719267918e-01;
Q7_9 = -2.3568822398349e-01;
Q7_10 =  6.9373143801571e-02;
Q7_11 = -1.6606121869177e-02;
Q7_12 =  2.5974025974031e-03;
Q7_13 = -1.8037518037522e-04;
Q7_14 =  0.0000000000000e+00;
Q7_15 =  0.0000000000000e+00;
Q7_16 =  0.0000000000000e+00;
Q7_17 =  0.0000000000000e+00;
Q8_0 = -1.1296706376589e-02;
Q8_1 =  2.9396383714543e-02;
Q8_2 = -4.3772338637753e-02;
Q8_3 =  6.0325702283960e-02;
Q8_4 = -7.4338719466734e-02;
Q8_5 =  4.4853791547749e-02;
Q8_6 =  1.5730779067906e-01;
Q8_7 = -8.0975719267918e-01;
Q8_8 =  0.0000000000000e+00;
Q8_9 =  8.4765775072084e-01;
Q8_10 = -2.6369594097148e-01;
Q8_11 =  7.8759594625702e-02;
Q8_12 = -1.7857142857146e-02;
Q8_13 =  2.5974025974031e-03;
Q8_14 = -1.8037518037522e-04;
Q8_15 =  0.0000000000000e+00;
Q8_16 =  0.0000000000000e+00;
Q8_17 =  0.0000000000000e+00;
Q9_0 =  3.1823678285130e-03;
Q9_1 = -8.5601827834256e-03;
Q9_2 =  1.3727655130726e-02;
Q9_3 = -2.1188913621662e-02;
Q9_4 =  3.1217656663809e-02;
Q9_5 = -3.2436468405486e-02;
Q9_6 = -2.6517620342970e-02;
Q9_7 =  2.3568822398349e-01;
Q9_8 = -8.4765775072084e-01;
Q9_9 =  0.0000000000000e+00;
Q9_10 =  8.5631774953989e-01;
Q9_11 = -2.6769768119702e-01;
Q9_12 =  7.9365079365093e-02;
Q9_13 = -1.7857142857146e-02;
Q9_14 =  2.5974025974031e-03;
Q9_15 = -1.8037518037522e-04;
Q9_16 =  0.0000000000000e+00;
Q9_17 =  0.0000000000000e+00;
Q10_0 = -2.4843594063649e-04;
Q10_0 = -2.4843594063649e-04;
Q10_1 =  7.8128092862319e-04;
Q10_1 =  7.8128092862319e-04;
Q10_2 = -1.6271304373071e-03;
Q10_2 = -1.6271304373071e-03;
Q10_3 =  3.2632650250470e-03;
Q10_3 =  3.2632650250470e-03;
Q10_4 = -6.1239492854797e-03;
Q10_4 = -6.1239492854797e-03;
Q10_5 =  8.4387621360184e-03;
Q10_5 =  8.4387621360184e-03;
Q10_6 =  4.3175367549700e-03;
Q10_6 =  4.3175367549700e-03;
Q10_7 = -6.9373143801571e-02;
Q10_7 = -6.9373143801571e-02;
Q10_8 =  2.6369594097148e-01;
Q10_8 =  2.6369594097148e-01;
Q10_9 = -8.5631774953989e-01;
Q10_9 = -8.5631774953989e-01;
Q10_10 =  0.0000000000000e+00;
Q10_10 =  0.0000000000000e+00;
Q10_11 =  8.5712580212095e-01;
Q10_11 =  8.5712580212095e-01;
Q10_12 = -2.6785714285718e-01;
Q10_12 = -2.6785714285718e-01;
Q10_13 =  7.9365079365093e-02;
Q10_13 =  7.9365079365093e-02;
Q10_14 = -1.7857142857146e-02;
Q10_14 = -1.7857142857146e-02;
Q10_15 =  2.5974025974031e-03;
Q10_15 =  2.5974025974031e-03;
Q10_16 = -1.8037518037522e-04;
Q10_16 = -1.8037518037522e-04;
Q10_17 =  0.0000000000000e+00;
Q10_17 =  0.0000000000000e+00;
Q11_0 = -3.1501105449828e-05;
Q11_0 = -3.1501105449828e-05;
Q11_1 =  6.0444181254875e-05;
Q11_1 =  6.0444181254875e-05;
Q11_2 = -1.7066984372933e-05;
Q11_2 = -1.7066984372933e-05;
Q11_3 = -1.3097937809499e-04;
Q11_3 = -1.3097937809499e-04;
Q11_4 =  4.5892226603067e-04;
Q11_4 =  4.5892226603067e-04;
Q11_5 = -8.5964292632428e-04;
Q11_5 = -8.5964292632428e-04;
Q11_6 = -1.1092605832824e-03;
Q11_6 = -1.1092605832824e-03;
Q11_7 =  1.6606121869177e-02;
Q11_7 =  1.6606121869177e-02;
Q11_8 = -7.8759594625702e-02;
Q11_8 = -7.8759594625702e-02;
Q11_9 =  2.6769768119702e-01;
Q11_9 =  2.6769768119702e-01;
Q11_10 = -8.5712580212095e-01;
Q11_10 = -8.5712580212095e-01;
Q11_11 =  0.0000000000000e+00;
Q11_11 =  0.0000000000000e+00;
Q11_12 =  8.5714285714289e-01;
Q11_12 =  8.5714285714289e-01;
Q11_13 = -2.6785714285718e-01;
Q11_13 = -2.6785714285718e-01;
Q11_14 =  7.9365079365093e-02;
Q11_14 =  7.9365079365093e-02;
Q11_15 = -1.7857142857146e-02;
Q11_15 = -1.7857142857146e-02;
Q11_16 =  2.5974025974031e-03;
Q11_16 =  2.5974025974031e-03;
Q11_17 = -1.8037518037522e-04;
Q11_17 = -1.8037518037522e-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;
%%%%%%%%%%%%%%%%%%%%%%%%%%%