Exponential convergence through linear finite element discretization of stratified subdomains

JOURNAL OF COMPUTATIONAL PHYSICS

卷:322

Article

Guddati, Murthy N.¹  Druskin, Vladimir²  Astaneh, Ali Vaziri¹ 

[1] North Carolina State Univ, Dept Civil Engn, Raleigh, NC 27695 USA

[2] Schlumberger Doll Res Ctr, Cambridge, MA 02139 USA

关键词: Optimal grids;    Pade approximants;    Dirichlet-to-Neumann maps;    Rational approximation;    Spectral element methods;   

DOI  :  10.1016/j.jcp.2016.06.045

来源: Elsevier

【 摘 要 】

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length finite element method (CFEM), the technique is linked to Pade approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of elements. This, combined with sparse computation associated with linear finite elements, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free