28 citations · 60 across the 10 of their papers we have counts for
10 papers
Solving parametric elliptic interface problems via interfaced operator network
Sidi Wu, Aiqing Zhu, Yifa Tang +1
Learning operators mapping between infinite-dimensional Banach spaces via neural networks has attracted a considerable amount of attention in recent years. In this paper, we propos…
Convergence of physics-informed neural networks applied to linear second-order elliptic interface problems
Sidi Wu, Aiqing Zhu, Yifa Tang +1
With the remarkable empirical success of neural networks across diverse scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. Howev…
Efficient Generation of Membrane and Solvent Tetrahedral Meshes for Ion Channel Finite Element Calculation
Zhen Chao, Sheng Gui, Benzhuo Lu +1
A finite element solution of an ion channel dielectric continuum model such as Poisson-Boltzmann equation (PBE) and a system of Poisson-Nernst-Planck equations (PNP) requires tetra…
An inverse averaging finite element method for solving the size-modified Poisson-Nernst-Planck equations in ion channel simulations
Ruigang Shen, Qianru Zhang, ang Benzhuo Lu
In this work, we introduce an inverse averaging finite element method (IAFEM) for solving the size-modified Poisson-Nernst-Planck (SMPNP) equations. Comparing with the classical Po…
Sparse Representation of Gaussian Molecular Surface
Sheng Gui, Minxin Chen, Benzhuo Lu
In this paper, we propose a model and algorithm for sparse representing Gaussian molecular surface. The original Gaussian molecular surface is approximated by a relatively small nu…
A Decoupling Two-grid Method for the Time-dependent Poisson-Nernst-Planck Equations
Ruigang Shen, Shi Shu, Ying Yang +1
We study a two-grid strategy for decoupling the time-dependent Poisson-Nernst-Planck equations describing the mass concentration of ions and the electrostatic potential. The comput…
Efficient and Qualified Mesh Generation for Gaussian Molecular Surface Using Piecewise Trilinear Polynomial Approximation
Tiantian Liu, Minxin Chen, Benzhuo Lu
Recent developments for mathematical modeling and numerical simulation of biomolecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in…
A Decoupling Two-Grid Method for the Steady-State Poisson-Nernst-Planck Equations
Ying Yang, Benzhuo Lu, Yan Xie
Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are prop…
A local approximation of fundamental measure theory incorporated into three dimensional Poisson-Nernst-Planck equations to account for hard sphere repulsion among ions
Yu Qiao, Benzhuo Lu, Minxin Chen
The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal comput…
Continuum Electromechanical Modeling of Protein-Membrane Interaction
Y. C. Zhou, Benzhuo Lu, Alemayehu A. Gorfe
A continuum electromechanical model is proposed to describe the membrane curvature induced by electrostatic interactions in a solvated protein-membrane system. The model couples th…