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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…
Convergent Compact Finite Difference Methods with Symmetric Matrices and Highest Possible Orders for Variable-Coefficient Elliptic Equations
Qiwei Feng, Bin Han, Michelle Michelle +1
For the -dimensional variable-coefficient Poisson problem subject to Dirichlet boundary conditions, we seek compact (i.e., -point) symmetric fi…
A High-Order, Pressure-Robust, and Decoupled Finite Difference Method for the Stokes Problem
Qiwei Feng, Bin Han, Michael Neilan
In this paper, we consider the Stokes problem with Dirichlet boundary conditions and the constant kinematic viscosity in an axis-aligned domain . We decouple the velocity $\…
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…