The finite element method in electromagnetics. 2nd ed. (English) Zbl 1001.78001

Jin, Jianming

New York, NY: Wiley. xxvi, 753 p. (2002).

Summary: Since the publication of the first edition [see the review in Zbl 0823.65124] of this book about eight years ago, much progress has been made in the development of the finite element method for the analysis of electromagnetics problems, especially in five areas. The first is the development of higher-order vector finite elements, which make it possible to obtain highly accurate and efficient solutions of vector wave equations. The second is the development of perfectly matched layers as an absorbing boundary condition. Although the perfectly matched layers were intended primarily for the time-domain finite-difference method, they have also found applications in the finite element simulations. The third is perhaps the development of hybrid techniques that combine the finite element and asymptotic methods for the analysis of large, complex problems that were unsolvable in the past. The fourth is further development of the finite element-boundary integral methods that incorporate fast integral solvers, such as the fast multipole method, to reduce the computational complexity associated with the boundary integral part. The last, but not least, is the development of the finite element method in the time domain for transient analysis. As a result of all these efforts, the finite element method has gained more popularity in the computational electromagnetics community and has become one of the preeminent simulation techniques for electromagnetics problems.
In this second edition, we have updated the subject matter and introduced new advances in finite element technology. Three new chapters have been added: Absorbing boundary conditions; Finite element analysis in the time domain: The method of moments and fast solvers.

MSC:

78-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to optics and electromagnetic theory
78M10	Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78Mxx	Basic methods for problems in optics and electromagnetic theory
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

finite element method; electromagnetics problems; absorbing boundary condition; finite element-boundary integral methods; method of moments; fast solvers

Citations:

Zbl 0823.65124