In contrast to the positive definite Helmholtz equation, the deceivingly similar looking
indefinite Helmholtz equation is difficult to solve using classical iterative methods. Simply …

The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …

Accurate predictions of the wave-dominated region of an acoustic field in a room can be
generated using wave-based computational methods. One such method is the finite element …

Along with finite differences and finite elements, spectral methods are one of the three main
methodologies for solving partial differential equations on computers. This book provides a …

Since the middle of the last century, computing power has increased sufficiently that the
direct numerical approximation of Maxwell's equations is now an increasingly important tool …

This book offers a comprehensive presentation of some of the most successful and popular
domain decomposition preconditioners for finite and spectral element approximations of …

This chapter is devoted to the finite element analysis of Helmholtz problems on bounded
domains. Speaking of “Finite Element Analysis,” we elaborate on the computational analysis …

We introduce some cheaper and faster variants of the classical additive Schwarz
preconditioner (AS) for general sparse linear systems and show, by numerical examples …

The development of numerical methods for solving the Helmholtz equation, which behaves
robustly with respect to the wave number, is a topic of vivid research. It was observed that …

The paper addresses the properties of finite element solutions for the Helmholtz equation.
The h-version of the finite element method with piecewise linear approximation is applied to …