Exponential convergence through linear finite element discretization of stratified subdomains

摘要: Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise novel finite element discretization that results exponential convergence pre-selected points. The key features of are (a) use midpoint integration to evaluate contribution matrices, and (b) an unconventional mapping mesh into complex space. Named complex-length method (CFEM), technique linked Pade approximants provide Dirichlet-to-Neumann maps thus solution specified points domain. Exponential facilitates drastic reduction number elements. This, combined with sparse computation associated linear elements, significant cost. paper presents basic ideas as well illustration its effectiveness for variety involving Laplace, Helmholtz elastodynamics equations.