Transparent boundary conditions for wave propagation on unbounded domains

The numerical solution of the time dependent wave equation in an unbounded domain generally leads to a truncation of this domain, which requires the introduction of an artificial boundary with associated boundary conditions. Such nonreflecting conditions ensure the equivalence between the solution of the original problem in the unbounded region and the solution inside the artificial boundary. We consider the acoustic wave equation and derive exact transparent boundary conditions that are local in time and can be directly used in explicit methods. These conditions annihilate wave harmonics up to a given order on a spherical artificial boundary, and we show how to combine the derived boundary condition with a finite difference method. The analysis is complemented by a numerical example in two spatial dimensions that illustrates the usefulness and accuracy of transparent boundary conditions.

Effective cell-centred time-domain Maxwell's equations numerical solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed. © 2004 Elsevier Inc. All rights reserved.