Name
Title | ||
|---|---|---|
The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes |
Abstract | ||
|---|---|---|
We extend the mimetic finite difference (MFD) method to the numerical treatment of magnetostatic fields problems in mixed div-curl form for the divergence-free magnetic vector potential. To accomplish this task, we introduce three sets of degrees of freedom that are attached to the vertices, the edges, and the faces of the mesh, and two discrete operators mimicking the curl and the gradient operator of the differential setting. Then, we present the construction of two suitable quadrature rules for the numerical discretization of the domain integrals of the div-curl variational formulation of the magnetostatic equations. This construction is based on an algebraic consistency condition that generalizes the usual construction of the inner products of the MFD method. We also discuss the linear algebraic form of the resulting MFD scheme, its practical implementation, and discuss existence and uniqueness of the numerical solution by generalizing the concept of logically rectangular or cubic meshes by Hyman and Shashkov to the case of unstructured polyhedral meshes. The accuracy of the method is illustrated by solving numerically a set of academic problems and a realistic engineering problem. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.jcp.2010.09.007 | J. Comput. Physics |
Keywords | Field | DocType |
mfd method,algebraic consistency condition,magnetostatics,numerical treatment,mimetic finite difference method,numerical discretization,div – curl equations,div-curl variational formulation,magnetostatic field problem,mfd scheme,polyhedral mesh,linear algebraic form,usual construction,mimetic finite differences,numerical solution,magnetostatic equation,finite difference,degree of freedom,inner product,quadrature rule,finite difference method,linear algebra | Discretization,Polygon mesh,Linear form,Mathematical analysis,Finite difference,Operator (computer programming),Finite difference method,Quadrature (mathematics),Curl (mathematics),Mathematics | Journal |
Volume | Issue | ISSN |
230 | 2 | Journal of Computational Physics |
Citations | PageRank | References |
16 | 1.17 | 16 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| K. Lipnikov | 1 | 521 | 57.35 |
| G. Manzini | 2 | 16 | 1.17 |
| franco brezzi | 3 | 109 | 18.11 |
| A. Buffa | 4 | 360 | 27.78 |