We have constructed a sequence of solutions of the Helmholtz equation forming an orthogonal sequence on a given surface. Coefficients of these functions depend on an explicit algebraic formulae from the coefficient of the surface. Moreover, for exterior Helmholtz equation we have constructed an explicit normal derivative of the Dirichlet Green function. In the same way the Dirichlet-to-Neumann ...

The paper presents an iterative algorithm for studying a nonlinear shallow-water wave equation. The equation is written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. We propose a two-step iterative method that first solves the evolution equation by the implicit midpoint rule and then solves the Helmholtz equation using a three-poi...

<p style='text-indent:20px;'>Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-iterative sampling method is proposed for detecting taking field measurements on bounded line segment above surface, based reconstructing modified near-field equation associated special which generalized our previous work Helmhol...

A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly...

We consider the parabolic approximation to the three{dimensional Helmholtz equation for the acoustic pressure. The parabolic equation is semi{discretized in the range variable using an implicit scheme (e.g., Crank{Nicolson). This leads to a complex elliptic partial di erential equation that must be solved at each range step. We use a multigrid method to solve this partial di erential equation, ...

A general theory of thermoacoustics is derived for arbitrary stack pores. Previous theoretical treatments of porous media are extended by considering arbitrarily shaped pores with the only restriction that the pore cross-sections vary slowly in the longitudinal direction. No boundary-layer approximation is necessary. Furthermore, the model allows temperature variations in the pore wall. By mean...

This paper applies one of the special cases auxiliary method, which is named as Bernoulli sub-equation function to nonlinear modified alpha equation. The characteristic properties these solutions, such complex and soliton are extracted. Moreover, strain conditions solutions also reported in detail. Observing figures plotted by considering various values parameters confirms effectiveness approxi...

We develop a High Order Fourier solver for nonseparable, selfadjoint elliptic equations with variable (diffusion) coefficients. The solution of an auxiliary constant coefficient equation, serves in a transformation of the dependent variable. There results a ”modified Helmholtz” elliptic equation with almost constant coefficients. The small deviations from constancy are treated as correction ter...