On partial spherical means formulas and radiation boundary conditions for the 3+1 wave equation

Reeectionless Boundary Propagation Formulas for Partial Wave Solutions to the Wave Equation

We consider solutions to the wave equation in 3+1 spacetime dimensions whose data is compactly supported at some initial time. For points outside a ball containing the initial support, we develop an outgoing wave condition, and associated one-way propagation formula, for the partial waves in the spherical-harmonic decomposition of the solution. The propagation formula expresses the l-th partial...

A urate Radiation Boundary Conditions for theTime - Dependent Wave Equation on

Absorbing boundary conditions for the wave equation and parallel computing

Absorbing boundary conditions have been developed for various types of problems to truncate infinite domains in order to perform computations. But absorbing boundary conditions have a second, recent and important application: parallel computing. We show that absorbing boundary conditions are essential for a good performance of the Schwarz waveform relaxation algorithm applied to the wave equati...

Radiation Boundary Conditions for the Two - Dimensional Wave Equation from a Variational Principle Jan

A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (non...

Numerical Absorbing Boundary Conditions for the Wave Equation

We develop a theory of difference approximations to absorbing boundary conditions for the scalar wave equation in several space dimensions. This generalizes the work of the author described in [8]. The theory is based on a representation of analytical absorbing boundary conditions proven in [8]. These conditions are defined by compositions of first-order, one-dimensional differential operators....