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

Abstract

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.

Source term method for binary neutron stars initial data

“…The general problem of solving Poisson equation on an irregular grid has been widely studied in the field of computational fluid dynamics and aerodynamics. Methods such as the finite element method [30,31], the boundary condition capturing method [32,33], and the immersed interface method [34] have been developed to solve the elliptic equation in irregular domains. In this paper, the source term method [1] will be applied to the Poisson equation for the fluid velocity potential in the BNS initial value problem.…”