Commit 720dcda8 authored by ppanchal's avatar ppanchal
Browse files

Speed improvement with global quadrature

parent 92300c5c
% Testing the force formula
% Testing convergence for some alpha values
alpha1 = acosh(10);
alpha2 = acosh(20);
force1 = [];
force2 = [];
for i = 1 : 500
force1 = [force1 Gsum(i,alpha1)];
force2 = [force2 Gsum(i,alpha2)];
end
figure;
plot(1:500,force1);
hold on;
plot(1:500,force2);
%alpha = acosh(1+x);
% Next plot
xvals = 0.001:0.001:0.01;
......@@ -3,6 +3,11 @@
close all; clc; clear;
addpath(genpath("../../"));
global X;
global W;
load('X','X');
load('W','W');
% Initializing parameters for the problem
N = 50;
%N = getenv('TESTVAR');
......
%function [] = force_cube_cube_ext(N)
close all; clc; clear;
addpath(genpath("../../"));
% Initializing parameters for the problem
%N = 20;
N = getenv('TESTVAR');
% Dimensions of the cube
L = [1,1,1];
%distances = [distances; offset];
% Mesh for the geometry
cube_vol_mesh = mshCube(N,L);
mesh_in = cube_vol_mesh.bnd;
cube_vol_mesh = mshCube(N/2.,L/2.);
mesh_out = cube_vol_mesh.bnd;
% Translate the outer cube
tx = 1;
ty = 3;
tz = 2;
dist = norm([tx ty tz]);
N_vtcs = size(mesh_out.vtx,1);
trans = [tx * ones(N_vtcs,1), ty * ones(N_vtcs,1), tz * ones(N_vtcs,1)];
mesh_out.vtx = mesh_out.vtx + trans;
% Join to create the final mesh
mesh = union(mesh_in,mesh_out);
figure;
plot(mesh);
title('Mesh');
%% BEM
% Definition of FEM spaces and integration rule
S1_Gamma = fem(mesh,'P1');
S0_Gamma = fem(mesh,'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
R = 1.1; % Cutoff radius, also used for the velocity field
g = @(X) (sqrt(sum(X.^2,2)) > R)*(1) + (sqrt(sum(X.^2,2)) <= R)*3;
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));
% Getting Neumann trace on the two distinct surfaces
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;
%%
% Classical formula for force evaluation
normals_in = mesh_in.nrm;
classical_force_in = 0.5 * sum( mesh_in.ndv .* Psi_in.^2.* normals_in, 1)
normals_out = mesh_out.nrm;
classical_force_out = 0.5 * sum( mesh_out.ndv .* Psi_out.^2.* normals_out, 1)
charge_in = sum( mesh_in.ndv .* Psi_in, 1)
charge_out = sum( mesh_out.ndv .* Psi_out, 1)
coulomb_force = charge_in * charge_out / 4 / pi / dist^2
%%
% Choice of velocity field for force computation
% Input = N X 3, output = N X 3
%Nu = @(X) (sum(X.*X,2)<=R*R).*[X(:,1)==X(:,1), 0 * X(:,1) , 0 * X(:,1)];
% Velocity fields for the far away cube
%Nux = @(X) (sum(X.*X,2)>R*R).*[X(:,1)==X(:,1), 0 * X(:,1) , 0 * X(:,1)];
%Nuy = @(X) (sum(X.*X,2)>R*R).*[0*X(:,1), X(:,2)==X(:,2) , 0 * X(:,1)];
%Nuz = @(X) (sum(X.*X,2)>R*R).*[0* X(:,1), 0 * X(:,1) , X(:,3)==X(:,3)];
% Velocity fields for the near cube
Nux = @(X) (sum(X.*X,2)<R*R).*[X(:,1)==X(:,1), 0 * X(:,1) , 0 * X(:,1)];
Nuy = @(X) (sum(X.*X,2)<R*R).*[0*X(:,1), X(:,2)==X(:,2) , 0 * X(:,1)];
Nuz = @(X) (sum(X.*X,2)<R*R).*[0* X(:,1), 0 * X(:,1) , X(:,3)==X(:,3)];
%Nu = @(X) (sum(X.*X,2)>R*R).*[X(:,1)==X(:,1), 0 * X(:,1) , 0 * X(:,1)];
%Nu = @(X) (sum(X.*X,2)<=R*R).*[0 * X(:,1), X(:,1)==X(:,1) , 0 * X(:,1)];
%Nu = @(X) (sum(X.*X,2)<=R*R).*[X(:,1)==X(:,1), 0 * X(:,1) , 0 * X(:,1)];
%Nu = @(X) (sum(X.*X,2)<=R*R).*[X(:,1)==X(:,1), 0 * X(:,1) , 0 * X(:,1)];
% Visualizing the velocity fields
figure;
plot(mesh);
hold on;
vtcs = S0_Gamma.dof;
vels = Nux(vtcs);
quiver3(vtcs(:,1),vtcs(:,2),vtcs(:,3),vels(:,1),vels(:,2),vels(:,3));
title('Perturbation field');
% Definition of the kernel for T2
kernelx = @(x,y,z) sum(z.*(Nux(x) - Nux(y)), 2)./(sqrt(sum(z.^2,2)).^3)/ (4*pi);
kernely = @(x,y,z) sum(z.*(Nuy(x) - Nuy(y)), 2)./(sqrt(sum(z.^2,2)).^3)/ (4*pi);
kernelz = @(x,y,z) sum(z.*(Nuz(x) - Nuz(y)), 2)./(sqrt(sum(z.^2,2)).^3)/ (4*pi);
t2matx = panel_oriented_assembly(mesh,kernelx,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))
forcex = dot(Psi,t2matx * Rho)
forcey = dot(Psi,t2maty * Rho)
forcez = dot(Psi,t2matz * Rho)
%forcevals = [forcevals; force];
str1 = "Cube_Cube_";
fname = append(str1
%end
\ No newline at end of file
......@@ -3,6 +3,11 @@
close all; clc; clear;
addpath(genpath("../../"));
global X;
global W;
load('X','X');
load('W','W');
% Initializing parameters for the problem
N = 30;
% Radius of spheres
......
%function [] = force_cube_cube_ext(N)
close all; clc; clear;
addpath(genpath("../../"));
% Initializing parameters for the problem
N = 30;
% Radius of spheres
Rad = 10;
% distance between the centers
% separation
s = 1e-6 * Rad;
dist = 2*Rad + s;
% Mesh for the geometry
mesh_in = mshSphere(N,Rad);
mesh_out = mesh_in;
% Translate the outer cube
N_vtcs = size(mesh_out.vtx,1);
trans = [dist * ones(N_vtcs,1), zeros(N_vtcs,1), zeros(N_vtcs,1)];
mesh_out.vtx = mesh_out.vtx + trans;
% Join to create the final mesh
mesh = union(mesh_in,mesh_out);
figure;
plot(mesh);
title('Mesh');
%%
% Definition of FEM spaces and integration rule
S1_Gamma = fem(mesh,'P1');
S0_Gamma = fem(mesh,'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 = 10;
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;
PI_g = g(S0_Gamma.dof);
plot(mesh,PI_g);
title('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;
%%
% Classical formula for force evaluation
normals_in = mesh_in.nrm;
classical_force_in = 0.5 * sum( mesh_in.ndv .* Psi_in.^2.* normals_in, 1)
% Alternative approach to calculating the integral shown above?
charge_in = sum( mesh_in.ndv .* Psi_in, 1)
normals_out = mesh_out.nrm;
classical_force_out = 0.5 * sum( mesh_out.ndv .* Psi_out.^2.* normals_out, 1)
charge_out = sum( mesh_out.ndv .* Psi_out, 1)
% Analytical formula for s -> 0
force_exact = force_spheres(dist,Rad,1,Vin-Vout)
coulomb_force = charge_in * charge_out / 4 / pi / dist^2
force_unit = charge_in * charge_out / 4 / pi / Rad^2;
force_ratio_unit =
force_ratio = norm(classical_force_in)/coulomb_force
force_ratio_analytic = force_identical_spheres(Rad/dist)
%%
% Choice of velocity field for force computation
% Input = N X 3, output = N X 3
% Velocity fields for the far away sphere
%Nux = @(X) (sum(X.*X,2)>R*R).*[X(:,1)==X(:,1), 0 * X(:,1) , 0 * X(:,1)];
%Nuy = @(X) (sum(X.*X,2)>R*R).*[0*X(:,1), X(:,2)==X(:,2) , 0 * X(:,1)];
%Nuz = @(X) (sum(X.*X,2)>R*R).*[0* X(:,1), 0 * X(:,1) , X(:,3)==X(:,3)];
% Velocity fields for the near sphere
Nux = @(X) (sum(X.*X,2)<R*R).*[X(:,1)==X(:,1), 0 * X(:,1) , 0 * X(:,1)];
Nuy = @(X) (sum(X.*X,2)<R*R).*[0*X(:,1), X(:,2)==X(:,2) , 0 * X(:,1)];
Nuz = @(X) (sum(X.*X,2)<R*R).*[0* X(:,1), 0 * X(:,1) , X(:,3)==X(:,3)];
% Visualizing the velocity fields
figure;
plot(mesh);
hold on;
vtcs = S0_Gamma.dof;
vels = Nux(vtcs);
quiver3(vtcs(:,1),vtcs(:,2),vtcs(:,3),vels(:,1),vels(:,2),vels(:,3));
title('Perturbation field');
% Definition of the kernel for T2
kernelx = @(x,y,z) sum(z.*(Nux(x) - Nux(y)), 2)./(sqrt(sum(z.^2,2)).^3)/ (4*pi);
t2matx = panel_oriented_assembly(mesh,kernelx,S0_Gamma,S0_Gamma);
sum(sum(t2matx))
forcex = dot(Psi,t2matx * Rho)
%forcevals = [forcevals; force];
%end
\ No newline at end of file
% Function to integrate on the 4 dimensional cube, hard coded n = 5
function integral = integrate4dim(f)
load('X','X');
load('W','W');
%load('X','X');
%load('W','W');
global X;
global W;
% w = [0.568888888888889;
% 0.478628670499367;
% 0.478628670499367;
......
......@@ -2,8 +2,8 @@
% the correct form. Implementation done for Triangle reference elements
function integral = sstri_integrate(kernel,hbasisx,hbasisy,chi_tau,chi_t,g_tau,g_t,relation)
integral = 0;
load('X','X');
load('W','W');
%load('X','X');
%load('W','W');
% definition for k3
% For vectorized operations X is assumed to be of size N X 4 where each
......
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