An improved partition of unity finite element model for diffraction problems

The partition of unity finite element method (PUFEM) is explored and improv ed to deal with practical diffraction problems efficiently. The use of plan e waves as an external function space allows an efficient implementation of an approximate exterior non-reflective boundary condition, improving the o riginal proposed by Higdon for general diffraction problems. A 'virtually' analytical integration procedure is introduced for multi-dimensional high-f requency problems which exhibits a dramatic decrease in the number of opera tions for a given error compared with standard integration methods. Suitabl e conjugate gradient type solvers for the whole range of wavenumbers are us ed, including such cases in which PUFEM can produce nearly singular matrice s caused by 'round-off' limits. Copyright (C) 2001 John Wiley & Sons, Ltd.