In this thesis, we propose and analyze a fast method for computing the solution of the Helmholtz equation in a bounded domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is first split into one–way wave equations which are then solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the soluti...

{ We modify the Green's formulation for In-SAR phase unwrapping by using the Green's function as a series in the eigenfunctions of the Helmholtz equation that ensures a closed-form solution using 2D FFT's.

Boundary elements method is well-suited for computational acoustics. The main profit it brings is reduction in number of unknowns compared to FEM. However, application of BEM to sound scattering problems has shown, that this advantage is lost in case of high frequency waves. High frequencies require larger number of elements which contradicts the initial purpose of using BEM in solvers and may ...

For wave propagation in a slowly varying waveguide, it is necessary to solve the Helmholtz equation in a domain that is much larger than the typical wavelength. Standard finite difference and finite element methods must resolve the small oscillatory behavior of the wave field and are prohibitively expensive for practical applications. A popular method is to approximate the waveguide by segments...

We use a meshless numerical method to analyze the eigenanalysis of thin circular membranes with degenerate boundary conditions, composed by different orientations and structures of stringers. The membrane eigenproblem is studied by solving the two-dimensional Helmholtz equation utilizing the method of fundamental solutions and domain decomposition technique as well. The method of singular value...

This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes ...

A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here. We consider equations of motion for incompressible flow (of Newtonian fluids) in the curl rotating co-ordinate system. Then the equation of momentum should be split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one. The irrotational...