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In Curve: Rearranged for speed. arc_length_fun is now a property of Curve. If it is not supplied, it is computed via the derivative and spline fitting. Switching to the arc length parameterization is much faster now. The new stuff can be tested with testArcLength.m (which should be deleted after that).
author Martin Almquist <martin.almquist@it.uu.se>
date Sun, 29 Nov 2015 22:23:09 +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)