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**Computational electromagnetism. Variational formulations, complementarity, edge elements.**
*(English)*
Zbl 0945.78001

Orlando, FL: Academic Press. xviii, 352 p. (1998).

An excellent book explaining at a very accessible level the fundamentals of the variational approach to the basic equations of the classical electromagnetic theory as well as some important numerical methods based on this approach.

After an introduction to the variational formulations of the Maxwell equations the author shows how the Galerkin method leads to finite element procedures suggesting a method for error analysis. This is the first part of the book (the first four chapters) devoted according to the author to the study of the “div-side” of electromagnetic models. In order to apply the same approach to the “curl-side” one needs the “correct” finite elements. For this reason the Whitney elements (often called Whitney forms) are introduced (Chapter 5) which include the standard node-based scalar elements, edge elements, face elements, etc. Some applications to magnetostatics problem and additional justification of these structures are then discussed in Chapter 6.

In Chapter 7 the infinite regions are considered where the integral methods on an artificial boundary in association with finite elements in a bounded domain are used. The applications of all this technique to the eddy-current problems and to the microwave oven model are considered in the last two chapters 8 and 9 of the book.

Three quite extensive appendices together with a good number of solved problems help to understand and to assimilate the material of the book which is a friendly guide to some profound ideas of mathematical physics and can be recommended not only to potential users of finite elements but to all students and researchers interested in advanced mathematical topics of electromagnetic theory.

After an introduction to the variational formulations of the Maxwell equations the author shows how the Galerkin method leads to finite element procedures suggesting a method for error analysis. This is the first part of the book (the first four chapters) devoted according to the author to the study of the “div-side” of electromagnetic models. In order to apply the same approach to the “curl-side” one needs the “correct” finite elements. For this reason the Whitney elements (often called Whitney forms) are introduced (Chapter 5) which include the standard node-based scalar elements, edge elements, face elements, etc. Some applications to magnetostatics problem and additional justification of these structures are then discussed in Chapter 6.

In Chapter 7 the infinite regions are considered where the integral methods on an artificial boundary in association with finite elements in a bounded domain are used. The applications of all this technique to the eddy-current problems and to the microwave oven model are considered in the last two chapters 8 and 9 of the book.

Three quite extensive appendices together with a good number of solved problems help to understand and to assimilate the material of the book which is a friendly guide to some profound ideas of mathematical physics and can be recommended not only to potential users of finite elements but to all students and researchers interested in advanced mathematical topics of electromagnetic theory.

Reviewer: Vladislav Kravchenko (MĂ©xico)