On wave boundary elements for radiation and scattering problems with piecewise constant impedance

• Published in: IEEE transactions on antennas and propagation Vol. 53; no. 2; pp. 876 - 879
• Main Authors: Perrey-Debain, E., Trevelyan, J., Bettess, P.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Boundary element methods; Boundary integral equation; Diffraction; Diffraction, scattering, reflection; Engineering Sciences; Exact sciences and technology; Finite element methods; Helmholtz equation; Impedance; Integral equations; Interpolation; Mathematics; Numerical analysis; plane waves; Radiocommunications; Radiowave propagation; Scattering; Shape; Telecommunications; Telecommunications and information theory; wave scattering; Freedom degree; Radiation scattering; Wave diffraction; Piecewise constant techniques; Helmholtz equation; impedance; Numerical method; Multiple wave; Finite element method; Interpolation; plane waves; Wave propagation; Boundary integral equation; Wave scattering; Plane wave; Boundary element method; Boundary integral equations
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2004.841274

Discrete methods of numerical analysis have been used successfully for decades for the solution of problems involving wave diffraction, etc. However, these methods, including the finite element and boundary element methods, can require a prohibitively large number of elements as the wavelength becomes progressively shorter. In this paper, a new type of interpolation for the wave field is described in which the usual conventional shape functions are modified by the inclusion of a set of plane waves propagating in multiple directions. Including such a plane wave basis in a boundary element formulation is found in this paper to be highly successful. Results are shown for a variety of scattering/radiating problems from convex and nonconvex obstacles on which are prescribed piecewise constant Robin conditions. Notable results include a conclusion that, using this new formulation, only approximately three degrees of freedom per wavelength are required.