Mixed E–B Finite Elements for Solving 1-D, 2-D, and 3-D Time-Harmonic Maxwell Curl Equations
نویسندگان
چکیده
Using a unified discretization approach based on differential forms, we describe mixed finite element methods (FEMs) in simplicial grids to solve time harmonic Maxwell curl equations in one-, two-, and three-dimensions. The proposed mixed FEM utilizes the electric field intensity and magnetic flux density as simultaneous state variables. Appropriate elements are used as interpolants for and to satisfy the interface conditions and a discrete version of the de Rham diagram.
منابع مشابه
Parallel Numerical Solution of the Time-Harmonic Maxwell Equations
We develop a fully scalable parallel implementation of an iterative solver for the time-harmonic Maxwell equations with vanishing wave numbers. We use a mixed finite element discretization on tetrahedral meshes, based on the lowest order Nédélec finite element pair of the first kind. We apply the block diagonal preconditioning approach of Greif and Schötzau (Numer. Linear Algebra Appl. 2007; 14...
متن کاملFinite Element Methods for Maxwell Equations
1. SOBOLEV SPACES AND WEAK FORMULATIONS Let Ω be a bounded Lipschitz domain in R. We introduce the Sobolev spaces H(curl ; Ω) = {v ∈ L(Ω), curlv ∈ L(Ω)}, H(div; Ω) = {v ∈ L(Ω),div v ∈ L(Ω)} The vector fields (E,H) belong to H(curl ; Ω) while the flux (D,B) in H(div; Ω). We shall use the unified notation H(d; Ω) with d = grad , curl , or div. Note that H(grad ; Ω) is the familiar H(Ω) space. The...
متن کاملA Locally Divergence-free Nonconforming Finite Element Method for the Reduced Time-harmonic Maxwell Equations
In this work, we will focus on (2), which will be referred to as the reduced time-harmonic Maxwell (RTHM) equations. Under the assumption that k is not a Maxwell eigenvalue, the RTHM equations have a unique solution in H0(curl; Ω) ∩H(div ; Ω). Our main achievement in this work is that we design a numerical method for RTHM equations using locally divergence-free Crouzeix-Raviart nonconforming P1...
متن کاملFinite Element Methods with Matching and Nonmatching Meshes for Maxwell Equations with Discontinuous Coefficients
We investigate the finite element methods for solving time-dependent Maxwell equations with discontinuous coefficients in general three-dimensional Lipschitz polyhedral domains. Both matching and nonmatching finite element meshes on the interfaces are considered, and optimal error estimates for both cases are obtained. The analysis of the latter case is based on an abstract framework for nested...
متن کاملOptimized Schwarz Methods for curl-curl time-harmonic Maxwell's equations
Like the Helmholtz equation, the high frequency time-harmonic Maxwell’s equations are difficult to solve by classical iterative methods. Domain decomposition methods are currently most promising: following the first provably convergent method in [4], various optimized Schwarz methods were developed over the last decade [2, 3, 10, 11, 1, 6, 13, 14, 16, 8]. There are however two basic formulation...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007