An improved partition of unity finite element model for diffraction problems

Abstract

AbstractThe partition of unity finite element method (PUFEM) is explored and improved to deal with practical diffraction problems efficiently. The use of plane waves as an external function space allows an efficient implementation of an approximate exterior non‐reflective boundary condition, improving the original proposed by Higdon for general diffraction problems. A ‘virtually’ analytical integration procedure is introduced for multi‐dimensional high‐frequency problems which exhibits a dramatic decrease in the number of operations for a given error compared with standard integration methods. Suitable conjugate gradient type solvers for the whole range of wavenumbers are used, including such cases in which PUFEM can produce nearly singular matrices caused by ‘round‐off’ limits. Copyright © 2001 John Wiley & Sons, Ltd.