(c) Vladimir Kazei, Oleg Ovcharenko, Dmitry Kabanov (KAUST, 2019)

This repository contains MATLAB implementation of the solver for the Helmholtz equation with absorbing boundary conditions (ABCs) and optional free surface.

The solver implements 1st and 2nd order ABCs (Clayton & Enquist, 1977) and 1st order BCs from the SimpleFWI project.

Figure below compares the numerical solutions obtained using the 1st and 2nd order ABCs with analytic Green's function:

We also add optional free surface to implementations of the boundary conditions of both orders:

The discretized Helmholtz equation is solved with a banded matrix solver, which is the most efficient for shallow and wide models.

The solver is written in MATLAB. To obtain the code, either download the code as ZIP archive or clone Git this repository via SSH:

    git clone [email protected]:vkazei/fastHelmholtz.git

or HTTPS:

    git clone https://github.com/vkazei/fastHelmholtz.git

and then open the code in MATLAB.

Core files
    getA - assemble Helmholtz matrix with 2nd order ABCs (optional free surface)
    getP - project solution to receiver positions
    F    - forward modeling

Reference files:
    getA_1st    - assemble Helmholtz matrix with 1st order ABCs
    getA_1st_FS - assemble Helmholtz matrix with 1st order ABCs and free surface

Misc files:
    defval  - assigns a default value to the named variable
    diags   - construct sparse diagonal matrix
    rdbuMap - custom colormap

Tests
    testHelmholtz    - test on homogeneous model
    testHelmholtz_FS - test on homogeneous model with free surface