相关论文: Explicit implementation strategy of high order edg…

In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations.The implementation of high order…

The time harmonic Maxwell equations are of current interest in computational science and applied mathematics with many applications in modern physics. In this work, we present parallel finite element solver for the time harmonic Maxwell…

This paper concerns the preconditioning technique for discrete systems arising from time-harmonic Maxwell equations with absorptions, where the discrete systems are generated by N\'ed\'elec finite element methods of fixed order on meshes…

This paper addresses the efficient solution of linear systems arising from curl-conforming finite element discretizations of $H(\mathrm{curl})$ elliptic problems with heterogeneous coefficients. We first employ the discrete form of a…

A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential…

Ill-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system…

We present a higher-order extension of the dual cell method for the time-domain Maxwell equations in three spatial dimensions. The approach builds upon a variational reinterpretation of the Finite Integration Technique on dual meshes and…

We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservative numerical formulations. High-order methods accurately…

The time-harmonic Maxwell equations are used to study the effect of electric and magnetic fields on each other. Although the linear systems resulting from solving this system using FEMs are sparse, direct solvers cannot reach the linear…

We propose a high order unfitted finite element method for solving timeharmonic Maxwell interface problems. The unfitted finite element method is based on a mixed formulation in the discontinuous Galerkin framework on a Cartesian mesh with…

In this paper, we design preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on FEM-SEM equivalence and additive Schwarz methods. The high-order…

We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…

This paper rigorously analyses preconditioners for the time-harmonic Maxwell equations with absorption, where the PDE is discretised using curl-conforming finite-element methods of fixed, arbitrary order and the preconditioner is…

The eXtended Finite Element Method (XFEM) is an approach for solving problems with non-smooth solutions. In the XFEM, the approximate solution is locally enriched to capture discontinuities without requiring a mesh which conforms to the…

We present a full-vector finite element method (FEM) mode solver for dielectric waveguides based on a mixed Nedelec-Lagrange discretization of Maxwell's curl equations in the frequency domain. The formulation combines edge elements for…

We shall propose and analyze some new preconditioners for the saddle-point systems arising from the edge element discretization of the time-harmonic Maxwell equations in three dimensions. We will first consider the saddle-point systems with…

This paper combines the use of high order finite element methods with parallel preconditioners of domain decomposition type for solving electromagnetic problems arising from brain microwave imaging. The numerical algorithms involved in such…

Edge (or N\'ed\'elec) finite elements are theoretically sound and widely used by the computational electromagnetics community. However, its implementation, specially for high order methods, is not trivial, since it involves many…

We propose a novel finite-difference time-domain (FDTD) scheme for the solution of the Maxwell's equations in which linear dispersive effects are present. The method uses high-order accurate approximations in space and time for the…

In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…