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Efficient algorithm and analysis for the Yang-Mills equations with temporal gauge
Ruiyang Li, Liqun Cao
This paper discusses the finite element method for the Yang-Mills equations with temporal gauge. The new contributions reported in this paper are threefold: an efficient linearized…
Efficient multiscale algorithms for simulating nonlocal optical response of metallic nanostructure arrays
Yongwei Zhang, Chupeng Ma, Liqun Cao +1
In this paper, we consider numerical simulations of the nonlocal optical response of metallic nanostructure arrays inside a dielectric host, which is of particular interest to the…
Multiscale Approach and The Convergence for the time-dependent Maxwell-Schrödinger System in Heterogeneous Nanostructures
Liqun Cao, Chupeng Ma, Jianlan Luo +1
This paper discusses the multiscale approach and the convergence of the time-dependent Maxwell-Schrödinger system with rapidly oscillating discontinuous coefficients arising from t…
A Crank-Nicolson Finite Element Method and the Optimal Error Estimates for the modified Time-dependent Maxwell-Schrödinger Equations
Chupeng Ma, Liqun Cao
In this paper we consider the initial-boundary value problem for the time-dependent Maxwell-Schrödinger equations, which arises in the interaction between the matter and the electr…
Error estimates of the Crank-Nicolson Galerkin method for the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge
Chupeng Ma, Liqun Cao, Yanping Lin
In this paper we study the numerical method and the convergence for solving the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge. An alternating Crank-Nicolson…
Mathematical and numerical analysis of the time-dependent Maxwell--Schrödinger Equations in the Coulomb gauge
Chupeng Ma, Liqun Cao, Jizu Huang +1
In this paper, we consider the initial-boundary value problem for the time-dependent Maxwell--Schrödinger equations in the Coulomb gauge. We first prove the global existence of wea…