@Article{CiCP-15-4,
author = {},
title = {A Kernel-Free Boundary Integral Method for Variable Coefficients Elliptic PDEs},
journal = {Communications in Computational Physics},
year = {2014},
volume = {15},
number = {4},
pages = {1108--1140},
abstract = {<p style="text-align: justify;">This work proposes a generalized boundary integral method for variable coefficients
elliptic partial differential equations (PDEs), including both boundary value
and interface problems. The method is kernel-free in the sense that there is no need
to know analytical expressions for kernels of the boundary and volume integrals in
the solution of boundary integral equations. Evaluation of a boundary or volume integral
is replaced with interpolation of a Cartesian grid based solution, which satisfies
an equivalent discrete interface problem, while the interface problem is solved by a
fast solver in the Cartesian grid. The computational work involved with the generalized
boundary integral method is essentially linearly proportional to the number
of grid nodes in the domain. This paper gives implementation details for a second-order
version of the kernel-free boundary integral method in two space dimensions
and presents numerical experiments to demonstrate the efficiency and accuracy of
the method for both boundary value and interface problems. The interface problems
demonstrated include those with piecewise constant and large-ratio coefficients and
the heterogeneous interface problem, where the elliptic PDEs on two sides of the interface
are of different types.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.170313.071113s},
url = {https://global-sci.com/article/80525/a-kernel-free-boundary-integral-method-for-variable-coefficients-elliptic-pdes}
}