The numerical manifold method for exterior problems

Abstract

The numerical manifold method (NMM), a Galerkin-type numerical method, has been successful in the solution of problems with finite definition domains, yet it has never been applied to problems with unbounded domains, or exterior problems. This study aims to fill the big gap by constructing infinite patches, together with the finite patches, to cover the unbounded domain. The local approximations of infinite patches can take the asymptotic estimations of the solutions at infinity, which are available for all those well-established boundary value problems. Compared with the infinite element methods in the finite element method (FEM), the construction of the trial functions by NMM is more elegant in theory and more systematical in methodology, resulting in more accurate solutions. Some typical examples in potential and half-space elasticity problems are investigated to illustrate the applicability and accuracy of the proposed method.