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Author Thompson, Lonny L. ♦ Huan, Runnong ♦ Ianculescu, Cristian
Source CiteSeerX
Content type Text
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Finite Element Formulation ♦ Extra Memory ♦ Direct Implementation ♦ Efficient Solution ♦ Spheroidal Coordinate ♦ Exact Dirichlet-to-neumann Radiation Condition ♦ Non-local Dtn Map ♦ Spheroidal Boundary ♦ Exact Dirichlet-to-neumann ♦ Iterative Solution ♦ Little Extra Cost ♦ Finite Element Implementation ♦ Dtn Boundary Condition ♦ Matrix-free Interpretation ♦ Finite Element Method ♦ Modified Dtn Condition ♦ Unbounded Domain ♦ Radiation Boundary Condition ♦ Dtn Map ♦ Helmholtz Equation ♦ Non-local Spatial Integral ♦ First Wave Harmonic ♦ Artificial Boundary ♦ Second Order Local Boundary Operator ♦ Form Suitable
Description Exact Dirichlet-to-Neumann (DtN) radiation boundary conditions are derived in elliptic and spheroidal coordinates and formulated in a finite element method for the Helmholtz equation in unbounded domains. The DtN map matches the first N wave harmonics exactly at the artificial boundary. The use of elliptic and spheroidal boundaries enables the efficient solution of scattering from elongated objects in two- and three- dimensions respectively. Modified DtN conditions based on first and second order local boundary operators are also derived in elliptic and spheroidal coordinates, in a form suitable for finite element implementation. The modified DtN conditions are more accurate than the DtN boundary condition, yet require no extra memory and little extra cost. Direct implementation involves non-local spatial integrals leading to a dense, fully populated submatrix. A matrix-free interpretation of the non-local DtN map for elliptic and spheroidal boundaries, suitable for iterative solution ...
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 1999-01-01
Publisher Institution Proceedings of the ASME Noise Control and Acoustics Division