Commit 892b22ff authored by ppanchal's avatar ppanchal
Browse files

tor tor test

parent 80b77ac3
......@@ -23,6 +23,7 @@ title('Pt convergence');
%%
% Checking the pt wise convergence of the trace
Rad = 5;
figure;
loglog(Nvals(1:sz-1),abs(Tn_plane(1:sz-1)+1/Rad));
hold on;
......
Nvals = Nvals';
sz = size(Nvals,1);
figure;
loglog(Nvals(1:sz-1),abs(averrs(1:sz-1)-averrs(sz)));
title('Av errors');
figure;
loglog(Nvals(1:sz-1),abs(l2errs(1:sz-1)-l2errs(sz)));
title('L2 errors');
figure;
loglog(Nvals(1:sz-1),abs(linferrs(1:sz-1)-linferrs(sz)));
title('Linf errors');
% Checking the pt wise convergence of the trace
figure;
loglog(Nvals(1:sz-1),abs(Tn_plane(1:sz-1)-Tn_plane(sz)));
hold on;
loglog(Nvals(1:sz-1),abs(Tn_nearest(1:sz-1)-Tn_nearest(sz)));
legend('Plane','Nearest DOF');
title('Pt convergence');
\ No newline at end of file
close all; clc; clear;
addpath(genpath("../../../"));
format long;
global X;
global W;
load('X3','X');
load('W3','W');
rng(10);
A = rand(3,3);
[Q,R] = qr(A);
% Initializing parameters for the problem
Nvals = 100:50:1700;
sz = size(Nvals,2);
l2errs = zeros(sz,1);
averrs = zeros(sz,1);
linferrs = zeros(sz,1);
Tn_nearest = zeros(sz,1);
Tn_plane = zeros(sz,1);
% Torus radii
r1 = 10;
r2 = 3;
N = 60;
for ii = 1:sz
N = Nvals(ii)
% distance between the centers
dist = 40;
% Mesh for the geometry
mesh_in = mshTorus(N,r1,r2);
mesh_out = mesh_in;
% Rotate the outer torus
mesh_out.vtx = mesh_out.vtx * Q;
% Translate the outer torus
N_vtcs = size(mesh_out.vtx,1);
trans = ones(N_vtcs,1) * [dist 0 0];
mesh_out.vtx = mesh_out.vtx + trans;
% Join to create the final mesh
mesh = union(mesh_in,mesh_out);
figure;
plot(mesh);
title('Mesh and normals');
hold on;
% Checking the normal direction for the mesh
ctrs = mesh.ctr;
nrms = mesh.nrm;
quiver3(ctrs(:,1),ctrs(:,2),ctrs(:,3),nrms(:,1),nrms(:,2),nrms(:,3));
%%
% Definition of FEM spaces and integration rule
S1_Gamma = fem(mesh,'P1');
S0_Gamma = fem(mesh,'P0');
S0_Gamma_in = fem(mesh_in,'P0');
order = 3;
Gamma = dom(mesh,order);
Op_in = restriction(S0_Gamma,mesh_in);
Op_out = restriction(S0_Gamma,mesh_out);
% Solving a Direct first kind BVP to get the representation of the state
% V Psi = (0.5*M+K) g_N (Interior problem)
% V Psi = (-0.5*M+K) g_N (Exterior problem)
% Getting the Single Layer matrix V using Gypsilab implementation
Gxy = @(X,Y)femGreenKernel(X,Y,'[1/r]',0); % 0 wave number
V = 1/(4*pi)*integral(Gamma,Gamma,S0_Gamma,Gxy,S0_Gamma);
V = V + 1/(4*pi)*regularize(Gamma,Gamma,S0_Gamma,'[1/r]',S0_Gamma);
% Getting the Double Layer matrix K using Gypsilab implementation
GradG = cell(3,1);
GradG{1} = @(X,Y)femGreenKernel(X,Y,'grady[1/r]1',0);
GradG{2} = @(X,Y)femGreenKernel(X,Y,'grady[1/r]2',0);
GradG{3} = @(X,Y)femGreenKernel(X,Y,'grady[1/r]3',0);
K = 1/(4*pi)*integral(Gamma,Gamma,S0_Gamma,GradG,ntimes(S0_Gamma));
K = K +1/(4*pi)*regularize(Gamma,Gamma,S0_Gamma,'grady[1/r]',ntimes(S0_Gamma));
% Defining the mass matrix M
M = integral(Gamma,S0_Gamma,S0_Gamma);
% Defining the Dirichlet boundary condition
% Cutoff radius for the BC
%R = 1;
R = dist/2;
%assert(R < Rad + s);
Vin = 10;
Vout = 20;
g = @(X) (sqrt(sum(X.^2,2)) > R)* Vout + (sqrt(sum(X.^2,2)) <= R) * Vin;
% Checking the boundary condition
figure;
plot(mesh);
hold on;
plot(mesh,g(S0_Gamma.dof));
title('Dirichlet Boundary Condition');
colorbar;
% Constructing the RHS
g_N = integral(Gamma,S0_Gamma,g);
% Exterior problem
Psi = V\((-0.5 * M + K)* (M\g_N));
Psi_in = Op_in * Psi;
Psi_out = Op_out * Psi;
% Solving the adjoint problem to get the adjoint solution
Rho = V\(-0.5 * g_N);
% Visualizing the Neumann trace
dofs = S0_Gamma.dof;
normals = mesh.nrm;
sPsi = -2*Psi;
figure;
plot(mesh);
hold on;
quiver3(dofs(:,1),dofs(:,2),dofs(:,3),normals(:,1).*sPsi,normals(:,2).*sPsi,normals(:,3).*sPsi,0);
title('Field on the surface');
%quiver3(dofs(:,1),dofs(:,2),dofs(:,3),normals(:,1),normals(:,2),normals(:,3));
% Visualizing the charge density on the surface of the objects
figure;
plot(mesh);
hold on;
plot(mesh,Psi);
title("Surface charge density");
colorbar;
%% Checking the convergence of the Neumann trace at a point
testpt = [r1+r2 0 0];
dofs = S0_Gamma.dof;
Ndofs = size(dofs,1);
distances = vecnorm((dofs - ones(Ndofs,1) * testpt),2,2);
[min_d,min_ind] = min(distances);
Tn_nearest(ii) = Psi(min_ind)
min_d
dofs(min_ind,:)
%% Using the plane method
elts = mesh.elt;
vtcs = mesh.vtx;
Nelts = size(elts,1);
dist_elts = zeros(Nelts,1);
for i = 1:Nelts
dist_elts(i) = dist_plane(testpt,vtcs(elts(i,1),:),vtcs(elts(i,2),:),vtcs(elts(i,3),:));
end
[mind_plane,minind_plane] = min(dist_elts)
Tn_plane(ii) = Psi(minind_plane)
%% Exact solution
err_vec = Psi;
% L2 Error
l2errs(ii) = err_vec' * M * err_vec %norm(err_vec)
averrs(ii) = err_vec' * V * err_vec
linferrs(ii) = max(abs(err_vec))
close all;
end
save('dirichlet_sol_tor_tor.mat',"averrs","l2errs","Tn_plane","Tn_nearest","Nvals","linferrs");
\ No newline at end of file
Nvals = Nvals';
sz = size(Nvals,1);
figure;
loglog(Nvals,averrs);
title('Av errors');
figure;
loglog(Nvals,l2errs);
title('L2 errors');
figure;
loglog(Nvals,linferrs);
title('Linf errors');
% Checking the pt wise convergence of the trace
exact_val = -1/4/pi/36;
figure;
loglog(Nvals(1:sz-1),abs(Tn_plane(1:sz-1)-Tn_plane(sz)));
%loglog(Nvals,abs(Tn_plane-exact_val));
hold on;
loglog(Nvals(1:sz-1),abs(Tn_nearest(1:sz-1)-Tn_nearest(sz)));
%loglog(Nvals(1:sz),abs(Tn_nearest-exact_val));
legend('Plane','Nearest DOF');
title('Pt convergence');
\ No newline at end of file
......@@ -8,17 +8,31 @@ global W;
load('X3','X');
load('W3','W');
rng(10);
A = rand(3,3);
[Q,R] = qr(A);
plotting = false;
% Initializing parameters for the problem
Nvals = 100:50:1700;
sz = size(Nvals,2);
l2errs = zeros(sz,1);
averrs = zeros(sz,1);
linferrs = zeros(sz,1);
Tn_nearest = zeros(sz,1);
Tn_plane = zeros(sz,1);
% Torus radii
r1 = 10;
r2 = 3;
N = 60;
for N = 20:100:1500
N
for ii = 1:sz
N = Nvals(ii)
% distance between the centers
dist = 40;
......@@ -32,9 +46,6 @@ trans = ones(N_vtcs,1) * [dist 0 0];
mesh_out.vtx = mesh_out.vtx + trans;
% Rotate the inner torus
rng(10);
A = rand(3,3);
[Q,R] = qr(A);
mesh_in.vtx = mesh_in.vtx * Q;
% Join to create the final mesh
......@@ -175,18 +186,18 @@ kernelz = @(x,y,z) sum(z.*(Nuz(x) - Nuz(y)), 2)./(vecnorm(z,2,2).^3)/ (4*pi);
%t2matx = panel_oriented_assembly(mesh,kernelx,S0_Gamma,S0_Gamma);
%t2fopx = panel_oriented_assembly(mesh,karnalx,S0_Gamma,S0_Gamma);
t2maty = panel_oriented_assembly(mesh,kernely,S0_Gamma,S0_Gamma);
%t2maty = panel_oriented_assembly(mesh,kernely,S0_Gamma,S0_Gamma);
%t2matz = panel_oriented_assembly(mesh,kernelz,S0_Gamma,S0_Gamma);
%sum(sum(t2matx))
%torquex = dot(Psi,t2matx * Rho)
%forcex = dot(Psi,t2fopx * Rho)
torquey = dot(Psi,t2maty * Rho)
%torquey = dot(Psi,t2maty * Rho)
%torquez = dot(Psi,t2matz * Rho)
str1 = "Torus_Torus_";
fname = append(str1,int2str(N));
%str1 = "Torus_Torus_";
%fname = append(str1,int2str(N));
%save(fname);
%exit;
......
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