@Article{CiCP-33-3,
author = {Yaning, Xie and Shuwang, Li and Ying, Wenjun},
title = {A Fourth-Order Kernel-Free Boundary Integral Method for Interface Problems},
journal = {Communications in Computational Physics},
year = {2023},
volume = {33},
number = {3},
pages = {764--794},
abstract = {<p style="text-align: justify;">This paper presents a fourth-order Cartesian grid based boundary integral
method (BIM) for heterogeneous interface problems in two and three dimensional
space, where the problem interfaces are irregular and can be explicitly given by parametric curves or implicitly defined by level set functions. The method reformulates the
governing equation with interface conditions into boundary integral equations (BIEs)
and reinterprets the involved integrals as solutions to some simple interface problems
in an extended regular region. Solution of the simple equivalent interface problems for
integral evaluation relies on a fourth-order finite difference method with an FFT-based
fast elliptic solver. The structure of the coefficient matrix is preserved even with the
existence of the interface. In the whole calculation process, analytical expressions of
Green’s functions are never determined, formulated or computed. This is the novelty
of the proposed kernel-free boundary integral (KFBI) method. Numerical experiments
in both two and three dimensions are shown to demonstrate the algorithm efficiency
and solution accuracy even for problems with a large diffusion coefficient ratio.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0236},
url = {https://global-sci.com/article/90818/a-fourth-order-kernel-free-boundary-integral-method-for-interface-problems}
}