High-order finite element-integral equation coupling on embedded meshes

JOURNAL OF COMPUTATIONAL PHYSICS

卷:375

Article

Beams, Natalie N.¹  Klockner, Andreas²  Olson, Luke N.² 

[1] Univ Illinois, Dept Mech Sci & Engn, Urbana, IL USA

[2] Univ Illinois, Dept Comp Sci, Urbana, IL 61801 USA

关键词: Interface problem;    Fictitious domain;    Layer potential;    FEM-IE coupling;    Iterative methods;    Algebraic multigrid;   

DOI  :  10.1016/j.jcp.2018.08.032

来源: Elsevier

【 摘 要 】

This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or inhomogeneous jump conditions without modification and retains high-order convergence close to the embedded interface. We present finite element-integral equation (FE-IE) formulations for interior, exterior, and interface problems. The treatments of the exterior and interface problems are new. The resulting linear systems are solved through an iterative approach exploiting the second-kind nature of the IE operator combined with algebraic multigrid preconditioning for the FE part. Assuming smooth continuations of coefficients and right-hand-side data, we show error analysis supporting high-order accuracy. Numerical evidence further supports our claims of efficiency and high-order accuracy for smooth data. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free