A comparison of three mixed methods for the time-dependent Maxwell’s equations. (English) Zbl 0762.65081

Monk, Peter

SIAM J. Sci. Stat. Comput. 13, No. 5, 1097-1122 (1992).

The dispersions properties of the Lee-Madsen method are investigated analytically. The corresponding algorithm of R. L. Lee and N. K. Madsen [J. Comput. Phys. 88, No. 2, 284-304 (1990; Zbl 0703.65082)] is compared with two other mixed finite element methods due (in three dimensions) to J.-C. Nédélec [Numer. Math. 35, 315-341 (1980; Zbl 0419.65069)] and to the author [A mixed method for approximating Maxwell’s equations, J. Comput. Appl. Math. (to appear)].
The connection between the mixed finite element methods analyzed here and the standard finite difference method for Maxwell’s equations, developed by K. Yee [Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Ann. Prop. AP–16, 302-307 (1966)] is also shown.

Reviewer: E.V.Nicolau (Bucureşti)

MSC:

65Z05	Applications to the sciences
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q60	PDEs in connection with optics and electromagnetic theory
78A25	Electromagnetic theory (general)

Keywords:

comparison of methods; Maxwell’s equations; Lee-Madsen method; mixed finite element methods; finite difference method

Citations:

Zbl 0436.65087; Zbl 0703.65082; Zbl 0419.65069