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acoustic_helmholtz_solver.jl
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acoustic_helmholtz_solver.jl
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# helmholtz_pml1 is the simplified pml version. With (1+i\beta)k^2 u + \Delta u = -f.
function make_diff_operator(h,omega,vel,beta,Nx,Ny)
coef = (1 + im*beta) .* (h^2*omega.^2) ./ (vel.^2);
coef = coef - 4;
A = spzeros(Complex64, (Nx-2)*(Ny-2), (Nx-2)*(Ny-2));
# A = zeros((Nx-2)*(Ny-2),(Nx-2)*(Ny-2));
# Center area
for i = 2:Nx-3
for j = 2:Ny-3
ind_row = (j-1)*(Nx-2)+i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = 1;
A[ind_row,ind_row+1] = 1;
A[ind_row,ind_row-Nx+2] = 1;
A[ind_row,ind_row+Nx-2] = 1;
end
end
# Top
i = 1;
for j = 2:Ny-3
ind_row = (j-1)*(Nx-2)+i;
A[ind_row,ind_row] = coef[i+1,j+1];
# A[ind_row,ind_row-1] = 1;
A[ind_row,ind_row+1] = 1;
A[ind_row,ind_row-Nx+2] = 1;
A[ind_row,ind_row+Nx-2] = 1;
end
# Bottom
i = Nx-2;
for j = 2:Ny-3
ind_row = (j-1)*(Nx-2)+i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = 1;
# A[ind_row,ind_row+1] = 1;
A[ind_row,ind_row-Nx+2] = 1;
A[ind_row,ind_row+Nx-2] = 1;
end
# Left
j = 1;
for i = 2:Nx-3
ind_row = (j-1)*(Nx-2)+i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = 1;
A[ind_row,ind_row+1] = 1;
# A[ind_row,ind_row-Nx+2] = 1;
A[ind_row,ind_row+Nx-2] = 1;
end
# Right
j = Ny-2;
for i = 2:Nx-3
ind_row = (j-1)*(Nx-2)+i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = 1;
A[ind_row,ind_row+1] = 1;
A[ind_row,ind_row-Nx+2] = 1;
# A[ind_row,ind_row+Nx-2] = 1;
end
# Corner
i = 1; j = 1;
ind_row = (j-1)*(Nx-2)+i;
A[ind_row,ind_row] = coef[i+1,j+1];
# A[ind_row,ind_row-1] = 1;
A[ind_row,ind_row+1] = 1;
# A[ind_row,ind_row-Nx+2] = 1;
A[ind_row,ind_row+Nx-2] = 1;
i = Nx-2; j = 1;
ind_row = (j-1)*(Nx-2)+i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = 1;
# A[ind_row,ind_row+1] = 1;
# A[ind_row,ind_row-Nx+2] = 1;
A[ind_row,ind_row+Nx-2] = 1;
i = 1; j = Ny-2;
ind_row = (j-1)*(Nx-2)+i;
A[ind_row,ind_row] = coef[i+1,j+1];
# A[ind_row,ind_row-1] = 1;
A[ind_row,ind_row+1] = 1;
A[ind_row,ind_row-Nx+2] = 1;
# A[ind_row,ind_row+Nx-2] = 1;
i = Nx-2; j = Ny-2;
ind_row = (j-1)*(Nx-2)+i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = 1;
# A[ind_row,ind_row+1] = 1;
A[ind_row,ind_row-Nx+2] = 1;
# A[ind_row,ind_row+Nx-2] = 1;
return A;
end;
function acoustic_helmholtz_solver(vel,Nx,Ny,h,fre,source_vec,pml_len,pml_alpha,return_vec=true)
Nx_pml = Nx + 2pml_len;
Ny_pml = Ny + 2pml_len;
omega = fre * 2 * pi;
pml_value = linspace(0,pml_alpha,pml_len);
# (1+i\beta)k^2 u + \Delta u = -f.
beta = zeros(Nx_pml,Ny_pml);
for i = 1:pml_len
beta[pml_len+1-i,:] = pml_value[i];
beta[end-pml_len+i,:] = pml_value[i];
beta[:,pml_len+1-i] = pml_value[i];
beta[:,end-pml_len+i] = pml_value[i];
end
vel_ex = zeros(Nx_pml,Ny_pml);
vel_ex[pml_len+1:end-pml_len,pml_len+1:end-pml_len] = vel;
for i = 1:pml_len
vel_ex[i,:] = vel_ex[pml_len+1,:];
vel_ex[end-i+1,:] = vel_ex[end-pml_len,:];
vel_ex[:,i] = vel_ex[:,pml_len+1];
vel_ex[:,end-i+1] = vel_ex[:,end-pml_len];
end
# Source term
source = zeros(Complex64,Nx_pml-2,Ny_pml-2);
source[pml_len:pml_len-1+Nx,pml_len:pml_len-1+Ny] = reshape(source_vec,Nx,Ny);
source_vec = reshape(source, (Nx_pml-2)*(Ny_pml-2), 1);
# source_vec = -1*conj(source_vec);
source_vec = -1source_vec;
A = make_diff_operator(h,omega,vel_ex,beta,Nx_pml,Ny_pml);
u_vec = A\source_vec;
u = reshape(u_vec,Nx_pml-2,Ny_pml-2);
u = u[pml_len:pml_len-1+Nx,pml_len:pml_len-1+Ny];
if return_vec == true
u = reshape(u, Nx*Ny, 1);
end
return u;
end
function acoustic_helmholtz_solver_pml(vel,Nx,Ny,omega,h,source_vec,pml_len,pml_alpha,return_vec=true)
Nx0 = Nx + 2pml_len;
Ny0 = Ny + 2pml_len;
# pml_alpha = pml_alpha * omega.^2 / (4*pi^2*20*maximum(abs.(vel))) * (100*h);
# println("pml alpha: ", pml_alpha)
# pml_alpha = 0.1;
pml_value = linspace(0,pml_alpha,pml_len);
# Extend velocity
vel_ex = zeros(Complex64,Nx0,Ny0);
for i in 1:pml_len
vel_ex[i,pml_len+1:pml_len+Ny] = vel[1,:];
vel_ex[pml_len+Nx+i , pml_len+1 : pml_len+Ny] = vel[end,:];
vel_ex[pml_len+1:pml_len+Nx,i] = vel[:,1];
vel_ex[pml_len+1 : pml_len+Nx , pml_len+Ny+i] = vel[:,end];
end
vel_ex[1:pml_len,1:pml_len] = vel[1,1];
vel_ex[1:pml_len,pml_len+Ny+1:end] = vel[1,end];
vel_ex[pml_len+Nx+1:end,1:pml_len] = vel[end,1];
vel_ex[pml_len+Nx+1:end,pml_len+Ny+1:end] = vel[end,end];
vel_ex[pml_len+1:pml_len+Nx, pml_len+1:pml_len+Ny] = vel;
# PML Coef
sigma_x = zeros(Complex64,Nx0,Ny0);
sigma_y = zeros(Complex64,Nx0,Ny0);
for i = 1:pml_len
sigma_x[pml_len+1-i,:] = pml_value[i];
sigma_x[pml_len+Nx+i,:] = pml_value[i];
sigma_y[:,pml_len+1-i] = pml_value[i];
sigma_y[:,pml_len+Ny+i] = pml_value[i];
end
# Sx = 1 ./ (ones(Complex64, Nx0, Ny0) - im .* sigma_x / omega);
# Sy = 1 ./ (ones(Complex64, Nx0, Ny0) - im .* sigma_y / omega);
Sx = 1 ./ (ones(Complex64, Nx0, Ny0) - im .* sigma_x / omega .* vel_ex);
Sy = 1 ./ (ones(Complex64, Nx0, Ny0) - im .* sigma_y / omega .* vel_ex);
coef = (omega./vel_ex).^2 - (2/h^2)*(Sx + Sy);
coef_x = zeros(Complex64,Nx0,Ny0);
coef_y = zeros(Complex64,Nx0,Ny0);
coef_x[2:end-1,2:end-1] = (Sx[2:end-1,2:end-1] .* (Sx[3:end,2:end-1]-Sx[1:end-2,2:end-1])) ./ (4*h.^2);
coef_x[1,:] = coef_x[2,:]; coef_x[end,:] = coef_x[end-1,:];
coef_x[:,1] = coef_x[:,2]; coef_x[:,end] = coef_x[:,end-1];
coef_y[2:end-1,2:end-1] = (Sy[2:end-1,2:end-1] .* (Sy[2:end-1,3:end]-Sy[2:end-1,1:end-2])) ./ (4*h.^2);
coef_y[1,:] = coef_y[2,:]; coef_y[end,:] = coef_y[end-1,:];
coef_y[:,1] = coef_y[:,2]; coef_y[:,end] = coef_y[:,end-1];
coef_x1 = coef_x + Sx.^2/h^2;
coef_x2 = -1*coef_x + Sx.^2/h^2;
coef_y1 = coef_y + Sy.^2/h^2;
coef_y2 = -1*coef_y + Sy.^2/h^2;
# build differential matrix
A = spzeros(Complex64,(Nx0-2)*(Ny0-2),(Nx0-2)*(Ny0-2));
for i = 2:Nx0-3
for j = 2:Ny0-3
ind_row = (j-1)*(Nx0-2) + i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = coef_x2[i+1,j+1];
A[ind_row,ind_row+1] = coef_x1[i+1,j+1];
A[ind_row,ind_row-Nx0+2] = coef_y2[i+1,j+1];
A[ind_row,ind_row+Nx0-2] = coef_y1[i+1,j+1];
end
end
# Top
i = 1;
for j = 2:Ny0-3
ind_row = (j-1)*(Nx0-2) + i;
A[ind_row,ind_row] = coef[i+1,j+1];
# A[ind_row,ind_row-1] = coef_x2[i+1,j+1];
A[ind_row,ind_row+1] = coef_x1[i+1,j+1];
A[ind_row,ind_row-Nx0+2] = coef_y2[i+1,j+1];
A[ind_row,ind_row+Nx0-2] = coef_y1[i+1,j+1];
end
# Bottom
i = Nx0-2;
for j = 2:Ny0-3
ind_row = (j-1)*(Nx0-2) + i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = coef_x2[i+1,j+1];
# A[ind_row,ind_row+1] = coef_x1[i+1,j+1];
A[ind_row,ind_row-Nx0+2] = coef_y2[i+1,j+1];
A[ind_row,ind_row+Nx0-2] = coef_y1[i+1,j+1];
end
# Left
j = 1;
for i = 2:Nx0-3
ind_row = (j-1)*(Nx0-2) + i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = coef_x2[i+1,j+1];
A[ind_row,ind_row+1] = coef_x1[i+1,j+1];
# A[ind_row,ind_row-Nx0+2] = coef_y2[i+1,j+1];
A[ind_row,ind_row+Nx0-2] = coef_y1[i+1,j+1];
end
# Right
j = Ny0-2;
for i = 2:Nx0-3
ind_row = (j-1)*(Nx0-2) + i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = coef_x2[i+1,j+1];
A[ind_row,ind_row+1] = coef_x1[i+1,j+1];
A[ind_row,ind_row-Nx0+2] = coef_y2[i+1,j+1];
# A[ind_row,ind_row+Nx0-2] = coef_y1[i+1,j+1];
end
# Top Left
i = 1; j = 1;
ind_row = (j-1)*(Nx0-2) + i;
A[ind_row,ind_row] = coef[i+1,j+1];
# A[ind_row,ind_row-1] = coef_x2[i+1,j+1];
A[ind_row,ind_row+1] = coef_x1[i+1,j+1];
# A[ind_row,ind_row-Nx0+2] = coef_y2[i+1,j+1];
A[ind_row,ind_row+Nx0-2] = coef_y1[i+1,j+1];
# Top Right
i = 1; j = Ny0-2;
ind_row = (j-1)*(Nx0-2) + i;
A[ind_row,ind_row] = coef[i+1,j+1];
# A[ind_row,ind_row-1] = coef_x2[i+1,j+1];
A[ind_row,ind_row+1] = coef_x1[i+1,j+1];
A[ind_row,ind_row-Nx0+2] = coef_y2[i+1,j+1];
# A[ind_row,ind_row+Nx0-2] = coef_y1[i+1,j+1];
# Bottom Left
i = Nx0-2; j = 1;
ind_row = (j-1)*(Nx0-2) + i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = coef_x2[i+1,j+1];
# A[ind_row,ind_row+1] = coef_x1[i+1,j+1];
# A[ind_row,ind_row-Nx0+2] = coef_y2[i+1,j+1];
A[ind_row,ind_row+Nx0-2] = coef_y1[i+1,j+1];
# Bottom Right
i = Nx0-2; j = Ny0-2;
ind_row = (j-1)*(Nx0-2) + i;
A[ind_row,ind_row] = coef[i+1,j+1];
A[ind_row,ind_row-1] = coef_x2[i+1,j+1];
# A[ind_row,ind_row+1] = coef_x1[i+1,j+1];
A[ind_row,ind_row-Nx0+2] = coef_y2[i+1,j+1];
# A[ind_row,ind_row+Nx0-2] = coef_y1[i+1,j+1];
# Source Term
source = zeros(Complex64,Nx0-2,Ny0-2);
# source_coor += pml_len;
# source_ind = source_coor[:,1]-1 + (source_coor[:,2]-2)*(Nx0-2);
# source[source_ind] = -1*source_func;
# source_vec = reshape(source, (Nx0-2)*(Ny0-2), 1);
source[pml_len:pml_len-1+Nx,pml_len:pml_len-1+Ny] = reshape(source_vec,Nx,Ny);
source_vec = reshape(source, (Nx0-2)*(Ny0-2), 1);
u_vec = A\source_vec;
# Iterative method
# u_vec = bicgstabl(A,source_vec);
u = reshape(u_vec,Nx0-2,Ny0-2);
u = u[pml_len:pml_len-1+Nx,pml_len:pml_len-1+Ny];
if return_vec == true
u = reshape(u, Nx*Ny, 1);
end
# received_data = u[receiver_coor[:,1]+(receiver_coor[:,2]-1)*Nx];
return u
end