Recent Advances in Applying Wave-Envelope Elements to Unbounded Wave Problems

Abstract

The development of efficient numerical models for unbounded wave problems presents a major challenge for computation. The use of discrete node-based or grid-based schemes requires a suitable anechoic termination at the edge of a finite computational region. The more compact and manageable the inner region, the more demanding the numerical treatment that is required on its boundary. This difficulty is circumvented by a variety of Boundary Element (BE) techniques which represent the exterior solution as a surface distribution of source terms. These identically satisfy the field equations and radiate rather than absorb acoustical energy. BE schemes are intrinsically non-local in space and result in fully populated coefficient matrices, negating to some extent the economies implicit in using a surface rather than a volume discretisation. Moreover, when applied in the time domain, they generate differential or integral equations which are non-local in time and space. Various techniques have be used to reduce or ameliorate the computationally demanding character of such solutions (e.g. Geers 1978, Givoli and Cohen 1995).