6 papers
Efficient and simple fourth-order compact finite difference methods for convection-diffusion-reaction equations on arbitrary curved domains
Qiwei Feng, Bin Han, Peter Minev
In this paper, we discuss the 2D convection-diffusion-reaction equation with variable smooth coefficients and the Dirichlet boundary condition on a complicated, thin, and curved do…
Galerkin Scheme Using Biorthogonal Wavelets on Intervals for Elliptic Interface Problems
Bin Han, Michelle Michelle
This paper presents a wavelet Galerkin method for solving elliptic interface problems of the form in , where is a smooth interface…
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…
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 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…
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…