TY - JOUR
T1 - A Direct Method for Solving Three-Dimensional Elliptic Interface Problems
AU - Gamage , Kumudu
AU - Peng , Yan
AU - Li , Zhilin
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 353
EP - 374
PY - 2024
DA - 2024/05
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1014
UR - https://global-sci.org/intro/article_detail/ijnam/23128.html
KW - Piecewise constant coefficients with a finite jump, elliptic interface problems, finite difference scheme.
AB - <p style="text-align: justify;">This paper presents a direct method for efficiently solving three-dimensional elliptic
interface problems featuring piecewise constant coefficients with a finite jump across the interface.
A key advantage of our approach lies in its avoidance of augmented variables, distinguishing
it from traditional methods. The computational framework relies on a finite difference scheme
implemented on a uniform Cartesian grid system. By utilizing a seven-point Laplacian for grid
points away from the interface, our method only requires coefficient modifications for grid points
located near or on the interface. Numerical experiments validate our method’s effectiveness.
Generally, it achieves second-order accuracy for both the solution and its gradient, measured in
the maximum norm, particularly effective in scenarios with moderate coefficient jumps. Extending
and building upon the recent work of [1] on 1D and 2D elliptic interfaces, our approach successfully
introduces a simpler method for extension into three dimensions. Notably, our proposed method
not only offers efficiency and accuracy but also enhances the simplicity of implementation, making
it accessible to non-experts in the field.</p>