A MATRIX-FREE INTERPRETATION OF THE NON-LOCAL DIRICHLET-TO-NEUMANN RADIATION BOUNDARY CONDITION

Abstract

This communication describes an efficient implementation of the non-local Dirichlet-to-Neumann (DtN) radiation boundary condition which arises in the solution of exterior problems in acoustics. Exterior problems in acoustics involve unbounded fluid domains whose finite element solution requires the introduction of a truncation boundary in order to obtain a finite computational domain. The non-local (DtN) condition is an exact non-reflecting boundary condition which is imposed on this truncation boundary. Unfortunately, the discretization of the non-local (DtN) boundary condition results in a dense, fully populated matrix whose storage and factorization become increasingly expensive. We describe here a matrix-free interpretation of the non-local (DtN) map suitable for iterative solution methods, which allows the use of this exact boundary condition without any storage penalties related to its non-local nature.