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view +util/calc_borrowing.m @ 99:ecf77a50d4fe feature/arclen-param

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The arclength parameter function was slow because it called fzero. Now it is constructed once and for all with splines. Much better performance.
author Martin Almquist <martin.almquist@it.uu.se>
date Sun, 06 Dec 2015 15:41:42 +0100
parents 48b6fb693025
children 03151dd46534
line wrap: on
line source


m = 30;
h = 1;


%% 4th order non-compatible
[H, HI, D1, D2, D3, D4, e_1, e_m, M, M4,Q, Q3, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = sbp.higher4(m,h);
S1 = S_1*S_1'  + S_m*S_m';
S2 = S2_1*S2_1' + S2_m*S2_m';
S3 = S3_1*S3_1' + S3_m*S3_m';

alpha_II  = util.matrixborrow(M4, h*S2  );
alpha_III = util.matrixborrow(M4, h^3*S3);
fprintf('4th order non-compatible\n')
fprintf('alpha_II:  %.10f\n',alpha_II)
fprintf('alpha_III: %.10f\n',alpha_III)
fprintf('\n')


%% 6th order non-compatible
[H, HI, D1, D2, D3, D4, e_1, e_m, M, M4,Q, Q3, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = sbp.higher6(m,h);
S1 = S_1*S_1'  + S_m*S_m';
S2 = S2_1*S2_1' + S2_m*S2_m';
S3 = S3_1*S3_1' + S3_m*S3_m';

alpha_II  = util.matrixborrow(M4, h*S2  );
alpha_III = util.matrixborrow(M4, h^3*S3);
fprintf('6th order non-compatible\n')
fprintf('alpha_II:  %.10f\n',alpha_II)
fprintf('alpha_III: %.10f\n',alpha_III)
fprintf('\n')


%% 2nd order compatible
[H, HI, D1, D4, e_1, e_m, M4, Q, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = sbp.higher2_compatible(m,h);
S1 = S_1*S_1'  + S_m*S_m';
S2 = S2_1*S2_1' + S2_m*S2_m';
S3 = S3_1*S3_1' + S3_m*S3_m';

alpha_II  = util.matrixborrow(M4, h*S2  );
alpha_III = util.matrixborrow(M4, h^3*S3);
fprintf('2nd order compatible\n')
fprintf('alpha_II:  %.10f\n',alpha_II)
fprintf('alpha_III: %.10f\n',alpha_III)
fprintf('\n')


%% 4th order compatible
[H, HI, D1, D4, e_1, e_m, M4, Q, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = sbp.higher4_compatible(m,h);
S1 = S_1*S_1'  + S_m*S_m';
S2 = S2_1*S2_1' + S2_m*S2_m';
S3 = S3_1*S3_1' + S3_m*S3_m';

alpha_II  = util.matrixborrow(M4, h*S2  );
alpha_III = util.matrixborrow(M4, h^3*S3);
fprintf('4th order compatible\n')
fprintf('alpha_II:  %.10f\n',alpha_II)
fprintf('alpha_III: %.10f\n',alpha_III)
fprintf('\n')

%% 6th order compatible
[H, HI, D1, D4, e_1, e_m, M4, Q, S2_1, S2_m, S3_1, S3_m, S_1, S_m] = sbp.higher6_compatible(m,h);
S1 = S_1*S_1'  + S_m*S_m';
S2 = S2_1*S2_1' + S2_m*S2_m';
S3 = S3_1*S3_1' + S3_m*S3_m';

alpha_II  = util.matrixborrow(M4, h*S2  );
alpha_III = util.matrixborrow(M4, h^3*S3);
fprintf('6th order compatible\n')
fprintf('alpha_II:  %.10f\n',alpha_II)
fprintf('alpha_III: %.10f\n',alpha_III)