13 citations · 33 across the 18 of their papers we have counts for
18 papers
Multiscale model reduction and two-level Schwarz preconditioner for H(curl) elliptic problems
Chupeng Ma, Yongwei Zhang
This paper addresses the efficient solution of linear systems arising from curl-conforming finite element discretizations of elliptic problems with heterogeneous…
Two-level Restricted Additive Schwarz preconditioner based on Multiscale Spectral Generalized FEM for Heterogeneous Helmholtz Problems
Chupeng Ma, Christian Alber, Robert Scheichl +1
We present and analyze a two-level restricted additive Schwarz (RAS) preconditioner for heterogeneous Helmholtz problems, based on a multiscale spectral generalized finite element…
Fast-convergent two-level restricted additive Schwarz methods based on optimal local approximation spaces
Arne Strehlow, Chupeng Ma, Robert Scheichl
This paper proposes a two-level restricted additive Schwarz (RAS) method for multiscale PDEs, built on top of a multiscale spectral generalized finite element method (MS-GFEM). The…
A Mixed Multiscale Spectral Generalized Finite Element Method
Christian Alber, Chupeng Ma, Robert Scheichl
We present a multiscale mixed finite element method for solving second order elliptic equations with general -coefficients arising from flow in highly heterogeneous por…
A unified framework for multiscale spectral generalized FEMs and low-rank approximations to multiscale PDEs
Chupeng Ma
This work presents an abstract framework for the design, implementation, and analysis of the multiscale spectral generalized finite element method (MS-GFEM), a particular numerical…
Scalable multiscale-spectral GFEM with an application to composite aero-structures
Jean Bénézech, Linus Seelinger, Peter Bastian +4
In this paper, the first large-scale application of multiscale-spectral generalized finite element methods (MS-GFEM) to composite aero-structures is presented. The crucial novelty…
Exponential convergence of a generalized FEM for heterogeneous reaction-diffusion equations
Chupeng Ma, Jens Markus Melenk
A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter , based on locally appro…
Wavenumber explicit convergence of a multiscale generalized finite element method for heterogeneous Helmholtz problems
Chupeng Ma, Christian Alber, Robert Scheichl
In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces for solving high-frequency heterogeneous Helmholtz problems is systematically stud…
Overlapping Schwarz methods with GenEO coarse spaces for indefinite and non-self-adjoint problems
Niall Bootland, Victorita Dolean, Ivan G. Graham +2
GenEO (`Generalised Eigenvalue problems on the Overlap') is a method for computing an operator-dependent spectral coarse space to be combined with local solves on subdomains to for…
Error estimates for fully discrete generalized FEMs with locally optimal spectral approximations
Chupeng Ma, Robert Scheichl
This paper is concerned with error estimates of the fully discrete generalized finite element method (GFEM) with optimal local approximation spaces for solving elliptic problems wi…
GenEO coarse spaces for heterogeneous indefinite elliptic problems
Niall Bootland, Victorita Dolean, Ivan G. Graham +2
Motivated by recent work on coarse spaces for Helmholtz problems, we provide in this paper a comparative study on the use of spectral coarse spaces of GenEO type for heterogeneous…
Novel design and analysis of generalized FE methods based on locally optimal spectral approximations
Chupeng Ma, Robert Scheichl, Tim Dodwell
In this paper, the generalized finite element method (GFEM) for solving second order elliptic equations with rough coefficients is studied. New optimal local approximation spaces f…
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…
Mathematical and numerical analysis of a nonlocal Drude model in nanoplasmonics
Chupeng Ma, Yongwei Zhang, Jun Zou
In this paper, we consider the frequency-domain Maxwell's equations coupled to a nonlocal Drude model which describes the nonlocal optical response in metallic nanostructures. We p…
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…