3 papers
math.NA2025
High-order, Compact, and Symmetric Finite Difference Methods for -Dimensional Elliptic Equations
Qiwei Feng, Bin Han, Michelle Michelle +1
This paper presents compact, symmetric, and high-order finite difference methods (FDMs) for the variable Poisson equation on a -dimensional hypercube. Our schemes produce symmet…
math.NA2025
An Efficient Finite Difference-Based PML Technique for Acoustic Scattering Problems
Bin Han, Jiwoon Sim
The acoustic scattering problem is modeled by the exterior Helmholtz equation, which is challenging to solve due to both the unboundedness of the domain and the high dispersion err…
math.NA2025
Convergent Sixth-order Compact Finite Difference Method for Variable-Coefficient Elliptic PDEs in Curved Domains
Bin Han, Jiwoon Sim
Finite difference methods (FDMs) are widely used for solving partial differential equations (PDEs) due to their relatively simple implementation. However, they face significant cha…