81 citations · 236 across the 19 of their papers we have counts for
19 papers
A Matrix Basis Formulation For The Green's Functions Of Maxwell's Equations And The Elastic Wave Equations In Layered Media
Wenzhong Zhang, Bo Wang, Wei Cai
A matrix basis formulation is introduced to represent the 3 x 3 dyadic Green's functions in the frequency domain for the Maxwell's equations and the elastic wave equation in layere…
Exponential convergence for multipole and local expansions and their translations for sources in layered media: three-dimensional Laplace equation
Bo Wang, Wenzhong Zhang, Wei Cai
In this paper, we prove the exponential convergence of the multipole and local expansions, shifting and translation operators used in fast multipole methods (FMMs) for 3-dimensiona…
Fast multipole method for 3-D Laplace equation in layered media
Bo Wang, Wen Zhong Zhang, Wei Cai
In this paper, a fast multipole method (FMM) is proposed for 3-D Laplace equation in layered media. The potential due to charges embedded in layered media is decomposed into a free…
A Path Integral Monte Carlo Method based on Feynman-Kac Formula for Electrical Impedance Tomography
Yijing Zhou, Wei Cai
A path integral Monte Carlo method (PIMC) based on Feynman-Kac formula for mixed boundary conditions of elliptic equations is proposed to solve the forward problem of electrical im…
Fast Multipole Method For 3-D Helmholtz Equation In Layered Media
Bo Wang, Wenzhong Zhang, Wei Cai
In this paper, a fast multipole method (FMM) is proposed to compute long-range interactions of wave sources embedded in 3-D layered media. The layered media Green's function for th…
Exponential convergence for multipole and local expansions and their translations for sources in layered media: 2-D acoustic wave
Wenzhong Zhang, Bo Wang, Wei Cai
In this paper, we will first give a derivation of the multipole expansion (ME) and local expansion (LE) for the far field from sources in general 2-D layered media and the multipol…
A hierarchical random compression method for kernel matrices
Duan Chen, Wei Cai
In this paper, we propose a hierarchical random compression method (HRCM) for kernel matrices in fast kernel summations. The HRCM combines the hierarchical framework of the H-matri…
What Is the Fractional Laplacian?
Anna Lischke, Guofei Pang, Mamikon Gulian +8
The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in math…
A Heterogeneous FMM for 2-D Layered Media Helmholtz Equation I: Two & Three Layers Cases
Min Hyung Cho, Jingfang Huang, Dangxing Chen +1
In this paper, we will introduce a new heterogeneous fast multipole method (H-FMM) for 2-D Helmholtz equation in layered media. To illustrate the main algorithm ideas, we focus on…
High Order Hierarchical Divergence-free Constrained Transport Finite Element Method for Magnetic Induction Equation
Wei Cai, Jun Hu, Shangyou Zhang
In this paper, we will use the interior functions of an hierarchical basis for high order elements to enforce the divergence-free condition of a magnetic field approxim…
Efficient and accurate computation of electric field dyadic Green's function in layered media
Min Hyung Cho, Wei Cai
Concise and explicit formulas for dyadic Green's functions, representing the electric and magnetic fields due to a dipole source placed in layered media, are derived in this paper.…
Adaptive Finite Element Method for fractional differential equations using Hierarchical Matrices
Xuan Zhao, Xiaozhe Hu, Wei Cai +1
A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-unifo…
Accurate and Efficient Nystrom Volume Integral Equation Method for the Maxwell equations for Multiple 3-D Scatterers
Duan Chen, Wei Cai, Brian Zinser +1
In this paper, we develop an accurate and efficient Nyström volume integral equation (VIE) method for the Maxwell equations for large number of 3-D scatterers. The Cauchy Principal…
Investigating the Selectivity of KcsA Channel by an Image Charge Solvation Method (ICSM) in Molecular Dynamics Simulations
Katherine Baker, Duan Chen, Wei Cai
In this paper, we study the selectivity of the potassium channel KcsA by a recently developed image-charge solvation method(ICSM) combined with molecular dynamics simulations. The…
Highly Accurate Nyström Volume Integral Equation Method for the Maxwell equations for 3-D Scatters
Duan Chen, Wei Cai, Brian Zinser
In this paper, we develop highly accurate Nyström methods for the volume integral equation (VIE) of the Maxwell equation for 3-D scatters. The method is based on a formulation of t…
Numerical Solution of the Robin Problem of Laplace Equations with a Feynman-Kac Formula and Reflecting Brownian Motions
Yijing Zhou, Wei Cai
In this paper, we present numerical methods to implement the probabilistic representation of third kind (Robin) boundary problem for the Laplace equations. The solution is based on…
Computation of Local Time of Reflecting Brownian Motion and Probabilistic Representation of the Neumann Problem
Yijing Zhou, Wei Cai, Elton Hsu
In this paper, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in R3 and its use in the probabilistic representation of the s…
Divergence-free H(div)-conforming hierarchical bases for magnetohydrodynamics (MHD)
Wei Cai, Jian Wu, Jianguo Xin
In order to solve the magnetohydrodynamics (MHD) equations with a -conforming element, a novel approach is proposed to ensure the exact divergen…
A parallel method for solving Laplace equations with Dirichlet data using local boundary integral equations and random walks
Chanhao Yan, Wei Cai, Xuan Zeng
In this paper, we will present a new approach for solving Laplace equations in general 3-D domains. The approach is based on a local computation method for the DtN mapping of the L…