Radiation boundary conditions for time-dependent waves based on complete plane wave expansions

Radiation boundary conditions for time-dependent waves based on complete plane wave expansions

We develop complete plane wave expansions for time-dependent waves in a halfspace and use them to construct arbitrary-order local radiation boundary conditions for the scalar wave equation and equivalent first order systems. We demonstrate that, unlike other local methods, boundary conditions based on complete plane wave expansions provide nearly uniform accuracy over long time intervals. This ...

Asymptotic and Exact Radiation Boundary Conditions for Time-dependent Scattering

Asymptotic and exact local radiation boundary conditions first derived by Hagstrom and Hariharan are reformulated as an auxiliary Cauchy problem for linear first-order systems of ordinary equations on the boundary for each harmonic on a circle or sphere in twoor three-dimensions, respectively. With this reformulation, the resulting radiation boundary condition involves first-order derivatives o...

Partial-wave expansions of angular spectra of plane waves.

Focused electromagnetic beams are frequently modeled by either an angular spectrum of plane waves or a partial-wave sum of spherical multipole waves. The connection between these two beam models is explored here. The partial-wave expansion of an angular spectrum containing evanescent components is found to possess only odd partial waves. On the other hand, the partial-wave expansion of an alter...

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

Eigenfunction Expansions for Second-Order Boundary Value Problems with Separated Boundary Conditions

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....