TY - JOUR
T1 - A Cartesian Grid-Based Boundary Integral Method for an Elliptic Interface Problem on Closely Packed Cells
AU - Wenjun Ying
JO - Communications in Computational Physics
VL - 4
SP - 1196
EP - 1220
PY - 2018
DA - 2018/06
SN - 24
DO - http://doi.org/10.4208/cicp.2018.hh80.05
UR - https://global-sci.org/intro/article_detail/cicp/12324.html
KW - Laplace equation, cell suspension, inclusion of grains, boundary integral method, Cartesian grid method, finite difference method, fast Fourier transform.
AB - <p style="text-align: justify;">In this work, we propose a second-order version and a fourth-order version
of a Cartesian grid-based boundary integral method for an interface problem of the
Laplace equation on closely packed cells. When the cells are closely packed, the boundary
integrals involved in the boundary integral formulation for the interface problem
become nearly singular. Direct evaluation of the boundary integrals has accuracy issues.
The grid-based method evaluates a boundary integral by first solving an equivalent,
simple interface problem on a Cartesian grid with a fast Fourier transform based
Poisson solver, then interpolating the grid solution to get values of the boundary integral
at discretization points of the interface. The grid-based method presents itself as
an alternative but accurate numerical method for evaluating nearly singular, singular
and hyper-singular boundary integrals. This work can be regarded as a further development
of the kernel-free boundary integral method [W.-J. Ying and C. S. Henriquez,
A kernel-free boundary integral method for elliptic boundary value problems, Journal
of Computational Physics, Vol. 227 (2007), pp. 1046-1074] for problems in unbounded
domains. Numerical examples with both second-order and fourth-order versions of
the grid-based method are presented to demonstrate accuracy of the method.</p>