finite and boundary element methods have been used by many authors to solve mathematicalphysics problems. however, the coupling of these two methods happens to be more efficient as it combinestheir merits. in this paper, the mathematical analysis of the coupling of finite and boundary element methodsfor the helmholtz equation is presented.

which describes stationary reaction-diffusion phenomena but is often also called Helmholtz equation in certain communities. For example in meteorology, the early seminal papers [48, 56] led an entire community to call equations of the form (2) Helmholtz equations, see for example [14]. Even standard texts in applied mathematics now sometimes use the term Helmholtz equation for both (1) and (2),...

Numerical solutions of the Helmholtz equation and the one-way Helmholtz equation are compared in the weak range dependence limit, where the overall range distance is increased while the range dependence is weakened. It is observed that the difference between the solutions of these two equations persists in this limit. The one-way Helmholtz equation involves a square root operator and it can be ...

we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...

Abstract. In this study, we consider new finite difference schemes for solving the Helmholtz equation. Novel difference schemes which do not introduce truncation error are presented, consequently the exact solution for the Helmholtz equation can be computed numerically. The most important features of the new schemes are that while the resulting linear system has the same simple structure as tho...

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations u...

The finite element method has been widely used to discretize the Helmholtz equation with various types of boundary conditions. The strong indefiniteness of the Helmholtz equation makes it difficult to establish stability estimates for the numerical solution. In particular, discontinuous Galerkin methods for Helmholtz equation with a high wave number result in very large matrices since they typi...