5 papers
A Structure-Preserving Scheme for the Time-Dependent Ginzburg-Landau Model with BCS Gap Coupling
Boyi Wang, Saurav Shenoy, Daniel Fortino +2
We propose a structure-preserving scheme for a hybrid model that couples the time-dependent Ginzburg-Landau (TDGL) equation of superconducting vortex dynamics and the nonlinear Bar…
Geometric local parameterization for solving Hele-Shaw problems with surface tension
Zengyan Zhang, Wenrui Hao, John Harlim
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented…
Optimal error estimates of the diffuse domain method for parabolic equations
Wenrui Hao, Lili Ju, Yuejin Xu
In this paper, we study the convergence behavior of the diffuse domain method (DDM) for solving a class of second-order parabolic partial differential equations with Neumann bounda…
An Adaptive Orthogonal Basis Method for Computing Multiple Solutions of Differential Equations with polynomial nonlinearities
Lin Li, Yangyi Ye, Huiyuan Li
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial no…
A numerical method for solving elliptic equations on real closed algebraic curves and surfaces
Wenrui Hao, Jonathan D. Hauenstein, Margaret H. Regan +1
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysi…