56 citations · 93 across the 8 of their papers we have counts for
7 papers · 1 filter
Adaptive pseudo-time methods for the Poisson-Boltzmann equation with Eulerian solvent excluded surface
Benjamin Jones, Sheik Ahmed Ullah, Siwen Wang +1
This work further improves the pseudo-transient approach for the Poisson Boltzmann equation (PBE) in the electrostatic analysis of solvated biomolecules. The numerical solution of…
A regularization approach for solving Poisson's equation with singular charge sources and diffuse interfaces
Siwen Wang, Arum Lee, Emil Alexov +1
Singular charge sources in terms of Dirac delta functions present a well-known numerical challenge for solving Poisson's equation. For a sharp interface between inhomogeneous media…
Unconditionally stable time splitting methods for the electrostatic analysis of solvated biomolecules
Leighton Wilson, Shan Zhao
This work introduces novel unconditionally stable operator splitting methods for solving the time dependent nonlinear Poisson-Boltzmann (NPB) equation for the electrostatic analysi…
A matched alternating direction implicit (ADI) method for solving the heat equation with interfaces
Shan Zhao
A novel Douglas alternating direction implicit (ADI) method is proposed in this work to solve a two-dimensional (2D) heat equation with interfaces. The ADI scheme is a powerful fin…
A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation
Lin Mu, Junping Wang, Xiu Ye +1
A weak Galerkin (WG) method is introduced and numerically tested for the Helmholtz equation. This method is flexible by using discontinuous piecewise polynomials and retains the ma…
Weak Galerkin Methods for Second Order Elliptic Interface Problems
Lin Mu, Junping Wang, Guowei Wei +2
Weak Galerkin methods refer to general finite element methods for PDEs in which differential operators are approximated by their weak forms as distributions. Such weak forms give r…