A finite-element framework for a mimetic finite-difference discretization of Maxwell's equations

12/05/2020
by   James H. Adler, et al.
0

Maxwell's equations are a system of partial differential equations that govern the laws of electromagnetic induction. We study a mimetic finite-difference (MFD) discretization of the equations which preserves important underlying physical properties. We show that, after mass-lumping and appropriate scaling, the MFD discretization is equivalent to a structure-preserving finite-element (FE) scheme. This allows for a transparent analysis of the MFD method using the FE framework, and provides an avenue for the construction of efficient and robust linear solvers for the discretized system. In particular, block preconditioners designed for FE formulations can be applied to the MFD system in a straightforward fashion. We present numerical tests which verify the accuracy of the MFD scheme and confirm the robustness of the preconditioners.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

05/15/2021

A new mixed finite-element method for the biharmonic problem

Fourth-order differential equations play an important role in many appli...
09/18/2019

A macroelement stabilization for multiphase poromechanics

Strong coupling between geomechanical deformation and multiphase fluid f...
11/20/2019

Balanced truncation model reduction for 3D linear magneto-quasistatic field problems

We consider linear magneto-quasistatic field equations which arise in si...
08/05/2017

FEMPAR: An object-oriented parallel finite element framework

FEMPAR is an open source object oriented Fortran200X scientific software...
07/14/2016

Finite Element Integration with Quadrature on the GPU

We present a novel, quadrature-based finite element integration method f...
04/29/2021

Parallel Projection – A New Return Mapping Algorithm for Finite Element Modeling of Shape Memory Alloys

We present a novel method for finite element analysis of inelastic struc...
12/27/2021

Robust approximation of generalized Biot-Brinkman problems

The generalized Biot-Brinkman equations describe the displacement, press...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.