An improved partition of unity finite element model for diffraction problems

The partition of unity nite element method (PUFEM) is explored and improved to deal with practical di raction problems e ciently. The use of plane waves as an external function space allows an e cient implementation of an approximate exterior non-re ective boundary condition, improving the original proposed by Higdon for general di raction problems. A `virtuallyʹ 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-o ʹ limits