Documentation.md

Documentation

helmholtz_solver

Solves the 2D absorbing Helmholtz equation using GMRES. The form of the Helmhotlz equation is

No preconditioning is used.

Syntax

[p, relres] = helmholtz_solver(sos_map, source, absorption, ...
    omega, pml_size, sigma_star, max_iter, checkpoint_frequency, tol, guess, dx)

Parameters

Parameter	Kind	Description
sos_map	2D array, scalar	The speed of sound map
source	2D array	The source term
absorption	2D array, scalar (default=0)	The absorption term
omega	scalar (default=1)	The angular frequency
pml_size	scalar (default=12)	The size of the PML in pixels
sigma_star	scalar (default=2)	The maximum amplitude of the PML $\sigma$ function
max_iter	scalar (default=1000)	The maximum number of iterations for the GMRES solver
checkpoint_frequency	scalar (default=1000)	The size of the Krylov subspace between restarts
tol	scalar (default=1e-6)	The tolerance for the GMRES solver
guess	2D array (default=zeros(N,N))	The initial guess for the solution
dx	scalar (default=1)	The spacing between pixels

Outputs

p: The solution to the Helmholtz equation

relres: The relative residual of the GMRES solver

kwave_solution

Solves the 2D absorbing Helmholtz equation as the steady state of the wave equation, using k-Wave. Note that k-Wave must be installed and added to the MATLAB path.

Syntax

 p = kwave_solution(L, sos_map, absorption_coeff_map, ...
    source_location, omega, min_sos, ~, cfl, roundtrips, dx)

Parameters

Parameter	Kind	Description
L	2D array, scalar	The size of the domain
sos_map	2D array, scalar	The speed of sound map
absorption_coeff_map	2D array, scalar	The absorption coefficient map
source_location	1d array of len=2	The location of the source term
omega	scalar	The angular frequency
min_sos	scalar	The minimum speed of sound, for stability calculations
cfl	scalar	The CFL number
roundtrips	scalar	The number of roundtrips to run to consider the wavefield in steady state
dx	scalar	The spacing between pixels

Output

p: The solution to the Helmholtz equation