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scalar_helmholtz_solver.jl
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scalar_helmholtz_solver.jl
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# This is the file for scalar Helmholtz solver
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(Complex128, (Nx-2)*(Ny-2), (Nx-2)*(Ny-2));
# 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 extend_area(vel, acq_fre)
# Extend the velocity and build the damping factor
pml_alpha = acq_fre.pml_alpha;
pml_len = acq_fre.pml_len;
Nx_pml = acq_fre.Nx_pml;
Ny_pml = acq_fre.Ny_pml;
pml_value = linspace(0,pml_alpha,pml_len);
# (1+i\beta)k^2 u + \Delta u = -f.
# beta is the damping factor
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
return beta, vel_ex
end
function change_source(source_multi, acq_fre)
# Change the source vector dimension to Nx_pml-2 * Ny_pml-2
Nx_pml = acq_fre.Nx_pml;
Ny_pml = acq_fre.Ny_pml;
fre_num = acq_fre.fre_num;
source_num = acq_fre.source_num;
# Source term
source_vec = zeros(Complex64, (Nx_pml-2)*(Ny_pml-2), fre_num, source_num);
for ind_fre = 1:fre_num
for ind_source = 1:source_num
source = zeros(Complex64,Nx_pml-2,Ny_pml-2);
source[pml_len:pml_len-1+Nx,pml_len:pml_len-1+Ny] = reshape(source_multi[:,ind_fre,ind_source],Nx,Ny);
# Here we have a -1 coefficient to correct the helmholtz equation
source_vec[:,ind_fre,ind_source] = reshape(-1*source, (Nx_pml-2)*(Ny_pml-2), 1);
end
end
return source_vec
end
function scalar_helmholtz_solver(vel, source_multi, acq_fre)
# This is the fundamental solver
# Both vel and source are matrix form with size Nx*Ny
Nx_pml = acq_fre.Nx_pml;
Ny_pml = acq_fre.Ny_pml;
pml_len = acq_fre.pml_len;
Nx = acq_fre.Nx;
Ny = acq_fre.Ny;
frequency = acq_fre.frequency;
omega = frequency * 2 * pi;
fre_num = acq_fre.fre_num;
source_num = acq_fre.source_num;
# Initialize
wavefield = zeros(Complex64,Nx*Ny,fre_num,source_num);
recorded_data = zeros(Complex64,Nx*Ny,fre_num,source_num);
# Extend area
beta, vel_ex = extend_area(vel, acq_fre);
# Source term
source_vec = change_source(source_multi, acq_fre);
for ind_fre = 1:fre_num
A = make_diff_operator(h,omega[ind_fre],vel_ex,beta,Nx_pml,Ny_pml);
F = lufact(A);
for ind_source = 1:source_num
source = source_vec[:,ind_fre,ind_source];
# u_vec = A\source;
u_vec = F\source;
u = reshape(u_vec,Nx_pml-2,Ny_pml-2);
u = u[pml_len:pml_len-1+Nx,pml_len:pml_len-1+Ny];
u = reshape(u, Nx*Ny, 1);
wavefield[:,ind_fre,ind_source] = u;
recorded_data[:,ind_fre,ind_source] = acq_fre.projection_op * u;
println("Frequency ", frequency[ind_fre], "Hz source ", ind_source, " complete.")
end
end
return wavefield, recorded_data
end
# This is a pml version. Just for fun.
# 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