Dirichlet-to-Neumann boundary conditions for multiple scattering problems
By Marcus J. Grote, Christoph Kirsch. 2004
139 citations recorded by the source corpus.
A Dirichlet-to-Neumann (DtN) condition is derived for the numerical solution of time-harmonic multiple scattering problems, where the scatterer consists of several disjoint components. It is obtained by combining contributions from multiple purely outgoing wave fields. The DtN condition yields an exact non-reflecting boundary condition for the situation, where the computational domain and its exterior artificial boundary consist of several disjoint components. Because each sub-scatterer can be enclosed by a separate artificial boundary, the computational effort is greatly reduced and becomes independent of the relative distances between the different sub-domains. The DtN condition naturally fits into a variational formulation of the boundary-value problem for use with the finite element method. Moreover, it immediately yields as a by-product an exact formula for the far-field pattern of the scattered field. Numerical examples show that the DtN condition for multiple scattering is as accurate as the well-known DtN condition for single scattering problems [J. Comput. Phys. 82 (1989) 172; Numerical Methods for Problems in Infinite Domains, Elsevier, Amsterdam, 1992], while being more efficient due to the reduced size of the computational domain.
Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering, Ocean Engineering
View Paper: https://www.semanticscholar.org/paper/73fdeb600a500a82cd4c63f6f81d70da1d1b249b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Atomic and Molecular Physics, and Optics
In Electrical and Electronic Engineering
In Ocean Engineering
Citations in the corpus
- Hitchhiker's guide to the fractional Sobolev spaces (2011, background): “equations, are now experiencing impressive applications in different subjects, such as, among others, the thin obstacle problem [87, 69], optimization [37], finance [26], phase transitions [2, 14, 88, 40, 45], stratified materials [83, 23, 24], anomalous diffusion [68, 98, 65], crystal dislocation [”
- From the long jump random walk to the fractional Laplacian (2009, background): “... in finance [CT04], in phase transitions [AB98, ABS98, CSM05, SV08b], in stratified materials [SV08a], in anomalous diffusion [MK00], in crystal dislocation [Tol97], in soft thin films [Kur06], in some models of semipermeable membranes and flame propagation [CRS08], in conservation laws [BKW01], ”