相关论文: Domain Decomposition Method for Maxwell's Equation…
This review article revisits and outlines the perfectly matched layer (PML) method and its various formulations developed over the past 25 years for the numerical modeling and simulation of wave propagation in unbounded media. Based on the…
This paper presents and evaluates a framework for the coupling of subdomain-local projection-based reduced order models (PROMs) using the Schwarz alternating method following a domain decomposition (DD) of the spatial domain on which a…
The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
Extreme learning machine (ELM) is a methodology for solving partial differential equations (PDEs) using a single hidden layer feed-forward neural network. It presets the weight/bias coefficients in the hidden layer with random values, which…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…
This study focuses on solving the numerical challenges of imposing absorbing boundary conditions for dynamic simulations in the material point method (MPM). To attenuate elastic waves leaving the computational domain, the current work…
In this paper we explore the possibility for solving the 3D Maxwell's equations in the presence of nonlinear and/or inhomogeneous material response. We propose using a hybrid approach which combines a bound- ary integral representation with…
This paper treats the time-harmonic electro-magnetic scattering or radiation problem governed by Maxwell's equations in an exterior weak Lipschitz domain divided into two disjoint weak Lipschitz parts We will present a solution theory using…
In this paper, we present a new multiscale domain decomposition algorithm for computing solutions of static Eikonal equations. The new method is an iterative two-scale method that uses a parareal-like update scheme in combination with…
In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation $-\Delta u - (k^2+ {\rm i} \varepsilon)u = f$, with absorption…
When the electromagnetic wave is incident on the periodic structures, in addition to the scattering field, some guided modes that are traveling in the periodic medium could be generated. In the present paper, we study the calculation of…
We analyze and develop numerical methods for time-harmonic wave scattering in metallic waveguide structures of infinite extent. We show that radiation boundary conditions formulated via projectors onto outgoing modes determine the…
The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences. Two localized exponential time differencing methods are…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
In the framework of a mixed finite element method, a structure-preserving formulation for incompressible magnetohydrodynamic (MHD) equations with general boundary conditions is proposed. A leapfrog-type temporal scheme fully decouples the…
The most popular methods for self-consistent simulation of fields interacting with charged species is using finite difference time domain (FDTD) methods together with Newton's laws of motion to evolve locations and velocities of particles.…
We present a numerical approach to the solution of elastic phonon scattering problems based on a frequency domain decomposition of the atomistic equations of motion and the use of perfectly matched layer or PML boundaries. Unlike MD…
We develop a non-overlapping domain decomposition method (DDM) for scalar wave scattering by periodic layered media. Our approach relies on robust boundary-integral equation formulations of Robin-to-Robin (RtR) maps throughout the frequency…