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| *.log | ||
| *.out | ||
| *.swp | ||
| *.asv | ||
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| @@ -1,9 +1,9 @@ | ||
| Name: geopdes | ||
| Version: 3.2.2 | ||
| Date: 2021-04-07 | ||
| Version: 3.4.0 | ||
| Date: 2024-07-24 | ||
| Author: Rafael Vazquez, Carlo de Falco | ||
| Maintainer: Rafael Vazquez | ||
| Title: Iso-Geometric Analysis | ||
| Description: A research tool for Iso-Geometric Analysis of PDEs | ||
| Depends: octave (>= 5.1), nurbs (>= 1.4.1) | ||
| Depends: octave (>= 6.4), nurbs (>= 1.4.1) | ||
| License: GPLv3 |
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34 changes: 34 additions & 0 deletions
34
geopdes/inst/examples/base/data_files/bilaplacian_Lshaped_g_nmnn_8patches.m
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| % TEST_PLATE_MIXED_BC_G_NMNN: data function for Neumann boundary condition. | ||
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| function g = bilaplacian_Lshaped_g_nmnn_8patches (x, y, ind) | ||
| [th, r] = cart2pol (x, y); | ||
| th = (th < 0).*(2*acos(-1) + th) + (th >= 0) .* th; | ||
| % f = @(z) sin(3*pi/2*z).^2 - z.^2 * sin(3*pi/2)^2; | ||
| z = 0.544483736782464; %z = fsolve(f, 0.5) The one on the left is more precise, computed with bisection method | ||
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| C1 = 1/(z-1)*sin(3*pi/2*(z-1)) - 1/(z+1)*sin(3*pi/2*(z+1)); | ||
| C2 = cos(3*pi/2*(z-1)) - cos(3*pi/2*(z+1)); | ||
| F1 = cos((z-1)*th) - cos((z+1)*th); | ||
| F2 = 1/(z-1)*sin((z-1)*th) - 1/(z+1)*sin((z+1)*th); | ||
| DF1 = -(z-1)*sin((z-1)*th)+(z+1)*sin((z+1)*th); | ||
| DF2 = cos((z-1)*th)-cos((z+1)*th); | ||
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| psi = C1*F1 - C2*F2; %C1 and C2 are constants | ||
| Dpsi = C1*DF1 - C2*DF2; | ||
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| switch (ind) | ||
| case {4} %n=(-1,0) | ||
| g = -((z+1)*r.^(z).* psi.*cos(th) - r.^z.*Dpsi.*sin(th)); | ||
| case {2,6} %n=(1,0) | ||
| g = (z+1)*r.^(z).* psi.*cos(th) - r.^z.*Dpsi.*sin(th); | ||
| case {1,3} %n=(0,-1) | ||
| g = -((z+1)*r.^(z).* psi.*sin(th) + r.^z.*Dpsi.*cos(th)); | ||
| case {5} %n=(0,1) | ||
| g = (z+1)*r.^(z).* psi.*sin(th) + r.^z.*Dpsi.*cos(th); | ||
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| otherwise | ||
| error ('g_nmnn: unknown reference number') | ||
| end | ||
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| end | ||
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21
geopdes/inst/examples/base/data_files/bilaplacian_rhs_Lshaped.m
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| function uex = bilaplacian_rhs_Lshaped (x, y) | ||
| [th, r] = cart2pol (x, y); | ||
| th = (th < 0).*(2*acos(-1) + th) + (th >= 0) .* th; | ||
| z = 0.544483736782464; | ||
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| C1 = 1/(z-1)*sin(3*pi/2*(z-1)) - 1/(z+1)*sin(3*pi/2*(z+1)); | ||
| C2 = cos(3*pi/2*(z-1)) - cos(3*pi/2*(z+1)); | ||
| F1 = cos((z-1)*th) - cos((z+1)*th); | ||
| F1_2 = -(z-1)^2*cos((z-1)*th) + (z+1)^2*cos((z+1)*th); | ||
| F1_4 = (z-1)^4*cos((z-1)*th) - (z+1)^4*cos((z+1)*th); | ||
| F2 = 1/(z-1)*sin((z-1)*th) - 1/(z+1)*sin((z+1)*th); | ||
| F2_2 = -(z-1)*sin((z-1)*th) + (z+1)*sin((z+1)*th); | ||
| F2_4 = (z-1)^3*sin((z-1)*th) - (z+1)^3*sin((z+1)*th); | ||
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| psi = C1*F1 - C2*F2; | ||
| psi2 = C1*F1_2 - C2*F2_2; | ||
| psi4 = C1*F1_4 - C2*F2_4; | ||
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| uex = (r.^(z-3)).*(((z-1)^2)*(((z+1)^2)*psi+psi2)+((z+1)^2)*psi2+psi4); | ||
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| end |
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16
geopdes/inst/examples/base/data_files/solution_bilaplacian_Lshaped.m
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| function uex = solution_bilaplacian_Lshaped (x, y) | ||
| [th, r] = cart2pol (x, y); | ||
| th = (th < 0).*(2*acos(-1) + th) + (th >= 0) .* th; | ||
| % f = @(z) sin(3*pi/2*z).^2 - z.^2 * sin(3*pi/2)^2; | ||
| z = 0.544483736782464; %z = fsolve(f, 0.5) The one on the left is more precise, computed with bisection method | ||
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| C1 = 1/(z-1)*sin(3*pi/2*(z-1)) - 1/(z+1)*sin(3*pi/2*(z+1)); | ||
| C2 = cos(3*pi/2*(z-1)) - cos(3*pi/2*(z+1)); | ||
| F1 = cos((z-1)*th) - cos((z+1)*th); | ||
| F2 = 1/(z-1)*sin((z-1)*th) - 1/(z+1)*sin((z+1)*th); | ||
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| psi = C1*F1 - C2*F2; %C1 and C2 are constants | ||
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| uex = r.^(z+1).* psi; | ||
| end | ||
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19
geopdes/inst/examples/base/data_files/solution_bilaplacian_Lshaped_grad.m
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| function graduex = solution_bilaplacian_Lshaped_grad (x, y) | ||
| graduex = zeros(2, size(x,1), size(x,2)); | ||
| [th, r] = cart2pol (x, y); | ||
| th = (th < 0).*(2*acos(-1) + th) + (th >= 0) .* th; | ||
| % f = @(z) sin(3*pi/2*z).^2 - z.^2 * sin(3*pi/2)^2; | ||
| z = 0.544483736782464; %z = fsolve(f, 0.5) The one on the left is more precise, computed with bisection method | ||
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| C1 = 1/(z-1)*sin(3*pi/2*(z-1)) - 1/(z+1)*sin(3*pi/2*(z+1)); | ||
| C2 = cos(3*pi/2*(z-1)) - cos(3*pi/2*(z+1)); | ||
| F1 = cos((z-1)*th) - cos((z+1)*th); | ||
| F2 = 1/(z-1)*sin((z-1)*th) - 1/(z+1)*sin((z+1)*th); | ||
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| psi = C1*F1 - C2*F2; %C1 and C2 are constants | ||
| Dpsi = C1*(-(z-1)*sin((z-1)*th)+(z+1)*sin((z+1)*th)) - C2*(cos((z-1)*th)-cos((z+1)*th)); | ||
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| graduex(1,:,:) = (z+1)*r.^(z).* psi.*cos(th) - r.^z.*Dpsi.*sin(th); | ||
| graduex(2,:,:) = (z+1)*r.^(z).* psi.*sin(th) + r.^z.*Dpsi.*cos(th); | ||
| end | ||
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36
geopdes/inst/examples/base/data_files/solution_bilaplacian_Lshaped_hessian.m
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| function hessian = solution_bilaplacian_Lshaped_hessian (x, y) | ||
| hessian = zeros(2,2,size(x,1), size(x,2)); | ||
| [th, r] = cart2pol (x, y); | ||
| th = (th < 0).*(2*acos(-1) + th) + (th >= 0) .* th; | ||
| z = 0.544483736782464; | ||
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| C1 = 1/(z-1)*sin(3*pi/2*(z-1)) - 1/(z+1)*sin(3*pi/2*(z+1)); | ||
| C2 = cos(3*pi/2*(z-1)) - cos(3*pi/2*(z+1)); | ||
| F1 = cos((z-1)*th) - cos((z+1)*th); | ||
| F2 = 1/(z-1)*sin((z-1)*th) - 1/(z+1)*sin((z+1)*th); | ||
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| psi = C1*F1 - C2*F2; %C1 and C2 are constants | ||
| Dpsi = C1*(-(z-1)*sin((z-1)*th)+(z+1)*sin((z+1)*th)) - C2*(cos((z-1)*th)-cos((z+1)*th)); | ||
| D2psi = C1*(-((z-1)^2)*cos((z-1)*th)+((z+1)^2)*cos((z+1)*th)) - C2*(-(z-1)*sin((z-1)*th)+(z+1)*sin((z+1)*th)); | ||
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| ur=(z+1)*r.^(z).*psi; | ||
| uth=r.^(z+1).*Dpsi; | ||
| urr=z*(z+1)*r.^(z-1).*psi; | ||
| uthr=(z+1)*r.^(z).*Dpsi; | ||
| uthth=r.^(z+1).*D2psi; | ||
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| uxr=cos(th).*urr-sin(th).*(r.*uthr-uth)./(r.^2); | ||
| uxth=-sin(th).*ur+cos(th).*uthr-cos(th).*uth./r-sin(th).*uthth./r; | ||
| uyr=sin(th).*urr+cos(th).*(r.*uthr-uth)./(r.^2); | ||
| uyth=cos(th).*ur+sin(th).*uthr-sin(th).*uth./r+cos(th).*uthth./r; | ||
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| uxx=cos(th).*uxr-sin(th).*uxth./r; | ||
| uxy=sin(th).*uxr+cos(th).*uxth./r; | ||
| uyy=sin(th).*uyr+cos(th).*uyth./r; | ||
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| hessian(1,1,:,:) = uxx; | ||
| hessian(1,2,:,:) = uxy; | ||
| hessian(2,1,:,:) = uxy; | ||
| hessian(2,2,:,:) = uyy; | ||
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| end |
48 changes: 48 additions & 0 deletions
48
geopdes/inst/examples/base/ex_bilaplacian_Lshaped_8patch.m
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| % PHYSICAL DATA OF THE PROBLEM | ||
| clear problem_data | ||
| problem_data.geo_name = 'geo_Lshaped_8patches.txt'; | ||
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| % Type of boundary conditions for each side of the domain | ||
| problem_data.nmnn_sides = []; | ||
| problem_data.drchlt_sides = [1 2 3 4 5 6]; | ||
| problem_data.weak_drchlt_sides = []; | ||
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| % Physical parameters | ||
| problem_data.c_diff = @(x, y) ones(size(x)); | ||
| % problem_data.grad_c_diff = @(x, y) cat (1, ... | ||
| % reshape (zeros(size(x)), [1, size(x)]), ... | ||
| % reshape (zeros(size(x)), [1, size(x)])); | ||
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| % Source and boundary terms | ||
| problem_data.f = @bilaplacian_rhs_Lshaped; | ||
| % problem_data.g = @(x, y, ind) bilaplacian_Lshaped_g_nmnn_8patches (x,y,ind); | ||
| problem_data.h = @(x, y, ind) solution_bilaplacian_Lshaped (x, y); | ||
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| % Exact solution (optional) | ||
| problem_data.uex = @(x, y) solution_bilaplacian_Lshaped (x, y); | ||
| problem_data.graduex = @(x, y) solution_bilaplacian_Lshaped_grad (x, y); | ||
| problem_data.hessuex = @(x, y) solution_bilaplacian_Lshaped_hessian (x, y); | ||
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| % DISCRETIZATION PARAMETERS | ||
| clear method_data | ||
| method_data.degree = [4 4]; % Degree of the splines | ||
| method_data.regularity = [2 2]; % Regularity of the splines | ||
| method_data.nsub = [16 16]; % Number of subdivisions of the coarsest mesh, with respect to the mesh in geometry | ||
| method_data.nquad = method_data.degree+1; % Points for the Gaussian quadrature rule | ||
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| [geometry, msh, space, u] = mp_solve_bilaplace_C1 (problem_data, method_data); | ||
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| [err_h2,~,~,err_h2s] = sp_h2_error (space, msh, u, problem_data.uex, problem_data.graduex, problem_data.hessuex) | ||
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| subplot(1,2,1) | ||
| npts = [51 51]; | ||
| sp_plot_solution (u, space, geometry, npts); shading interp; title('Computed solution') | ||
| vtk_pts = {linspace(0,1,npts(1)), linspace(0,1,npts(2))}; | ||
| subplot(1,2,2) | ||
| for iptc = 1:msh.npatch | ||
| F = reshape (geometry(iptc).map(vtk_pts), [2, npts]); | ||
| X = reshape (F(1,:), npts); Y = reshape (F(2,:), npts); | ||
| surf(X, Y, problem_data.uex(X,Y)); | ||
| hold on; shading interp | ||
| end | ||
| title('Exact solution') |
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| % PHYSICAL DATA OF THE PROBLEM | ||
| clear problem_data | ||
| problem_data.geo_name = 'geo_hyperboloid_ASG1.txt'; | ||
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| % Type of boundary conditions for each side of the domain | ||
| problem_data.nmnn_sides = []; | ||
| problem_data.drchlt_sides = [1 2 3 4 5 6]; | ||
| problem_data.weak_drchlt_sides = []; | ||
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| % Physical parameters | ||
| problem_data.c_diff = @(x, y, z) ones(size(x)); | ||
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| % Source and boundary terms | ||
| C = 1; | ||
| p = -1; | ||
| cons = 200; | ||
| problem_data.f = @(x, y, z) 16.*cons.*exp(1).^((-1).*cons.*(x.^2+y.^2+(x.^2+(-1).*y.^2).^2)).* ... | ||
| (1+4.*x.^2+4.*y.^2).^(-5).*(cons.^3.*(1+4.*x.^2+4.*y.^2).^3.*(4.* ... | ||
| x.^6+(-4).*x.^4.*((-1)+y.^2)+(y+2.*y.^3).^2+x.^2.*(1+8.*y.^2+(-4) ... | ||
| .*y.^4)).^2+8.*(64.*x.^8+x.^6.*(32+(-896).*y.^2)+2.*x.^4.*(7+(-48) ... | ||
| .*y.^2+832.*y.^4)+y.^2.*((-1)+14.*y.^2+32.*y.^4+64.*y.^6)+(-1).* ... | ||
| x.^2.*(1+60.*y.^2+96.*y.^4+896.*y.^6))+(-4).*cons.^2.*(1+4.*x.^2+ ... | ||
| 4.*y.^2).^2.*(72.*x.^10+20.*x.^8.*(5+2.*y.^2)+x.^6.*(50+272.*y.^2+ ... | ||
| (-112).*y.^4)+(y+2.*y.^3).^2.*(1+7.*y.^2+18.*y.^4)+x.^4.*(11+142.* ... | ||
| y.^2+280.*y.^4+(-112).*y.^6)+x.^2.*(1+26.*y.^2+142.*y.^4+272.* ... | ||
| y.^6+40.*y.^8))+2.*cons.*(1+1568.*x.^10+19.*y.^2+174.*y.^4+796.* ... | ||
| y.^6+1752.*y.^8+1568.*y.^10+8.*x.^8.*(219+404.*y.^2)+4.*x.^6.*( ... | ||
| 199+1064.*y.^2+2896.*y.^4)+2.*x.^4.*(87+786.*y.^2+3720.*y.^4+ ... | ||
| 5792.*y.^6)+x.^2.*(19+244.*y.^2+1572.*y.^4+4256.*y.^6+3232.*y.^8))); | ||
| problem_data.h = @(x, y, z, ind) exp(-cons*(x.^2 + y.^2 + (x.^2 - y.^2).^2)); | ||
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| % Exact solution | ||
| problem_data.uex = @(x, y, z) exp(-cons*(x.^2 + y.^2 + (x.^2 - y.^2).^2)); | ||
| problem_data.graduex = @(x, y, z) cat (1, ... | ||
| reshape ( (-2).*cons.*exp(1).^((-1).*cons.*(x.^2+y.^2+(x.^2+(-1).*y.^2).^2)).*x.*(1+4.*x.^2+4.*y.^2).^(-1).*(1+2.*x.^2+6.*y.^2), [1, size(x)]), ... | ||
| reshape ( (-2).*cons.*exp(1).^((-1).*cons.*(x.^2+y.^2+(x.^2+(-1).*y.^2).^2)).*y.*(1+6.*x.^2+2.*y.^2).*(1+4.*x.^2+4.*y.^2).^(-1), [1, size(x)]), ... | ||
| reshape ( (-4).*cons.*exp (1).^((-1).*cons.*(x.^2+y.^2+(x.^2+(-1).*y.^2).^2)).*(1+4.*x.^2+4.*y.^2).^(-1).*(x.^2+2.*x.^4+(-1).*y.^2+(-2).*y.^4), [1, size(x)])); | ||
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| problem_data.lapuex = @(x, y, z) 4.*cons.*exp(1).^((-1).*cons.*(x.^2+y.^2+(x.^2+(-1).*y.^2).^2)).*( ... | ||
| 1+4.*x.^2+4.*y.^2).^(-2).*((-1)+20.*cons.*x.^6+16.*cons.*x.^8+(( ... | ||
| -8)+cons).*y.^2+4.*((-5)+2.*cons).*y.^4+20.*cons.*y.^6+16.*cons.* ... | ||
| y.^8+x.^2.*((-8)+cons+(-24).*y.^2+16.*cons.*y.^2+44.*cons.*y.^4)+( ... | ||
| -4).*x.^4.*(5+cons.*((-2)+(-11).*y.^2+8.*y.^4))); | ||
|
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| % DISCRETIZATION PARAMETERS | ||
| clear method_data | ||
| deg = 3; | ||
| method_data.degree = [deg deg]; % Degree of the splines | ||
| method_data.regularity = [deg-2 deg-2]; % Regularity of the splines | ||
| method_data.nsub = [16 16]; % Number of subdivisions of the coarsest mesh, with respect to the mesh in geometry | ||
| method_data.nquad = [deg+1 deg+1]; % Points for the Gaussian quadrature rule | ||
|
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| [geometry, msh, space, u] = mp_solve_bilaplace_C1 (problem_data, method_data); | ||
| npts = [41 41]; | ||
| sp_plot_solution (u, space, geometry); shading interp; axis equal | ||
| fprintf('Error in (equivalent) H2 seminorm = %g\n', sp_h2_equiv_lap_error(space, msh, u, problem_data.uex, problem_data.graduex, problem_data.lapuex)); |
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