Computational micromagnetism (Q2760409)

According to the author's preface, the object of this book is to summarize his researches in the field of computational ferromagnetism over the last four years and to connect them with recent work in the field by others. The book opens with a five-page list of symbols used, and the text is divided into two parts, the first on numerical stationary micromagnetism and the second on non-stationary phenomena. Each of the two parts is preceded by a summary and discussion of the results obtained in it. NEWLINENEWLINENEWLINEThe first chapter is entitled `Direct minimization'. A functional is developed and the associated error analysis for approximations associated with axial ferromagnets and cubic ferromagnets is developed. In the second chapter, on convexified 'Micromagnetism', the discretization of the equations and the associated numerical realizations are discussed. These subjects are illustrated by some diagrams. The title of the third chapter is `Relaxed micromagnetism using Young measures'. In this chapter some approximations using finite elements are introduced and the results of some numerical experiments are considered. NEWLINENEWLINENEWLINEThe fourth chapter discusses the Landau-Lifshitz-Gilbert equation. After analysing the equation the author considers its discretization and proceeds to discuss numerical solutions using finite elements and gives the results of some numerical experiments. In the fifth chapter the author goes on to consider how the phenomena involved are affected by modifying the equations involved by the addition of Maxwell's equations. Some time-splitting schemes are referred to and some computational experiments are considered. The sixth chapter is concerned with a slightly different subject, nematic crystals, involving consideration of the Ericksen-Leslie equations. Amongst other matters, this chapter provides existence theory and error analysis for the suggested methods of solution and an analysis of some numerical experiments. The seventh chapter gives a short summary of the most important parts of the book and suggestions for further work. The book closes with a list of 132 references, two thirds of which are after 1990. Surprisingly, in view of the author's nationality, and the places where he has worked, only one is in German! NEWLINENEWLINENEWLINEWhen one considers the book as a whole, there is much in it which will not be found in other books, summarizing the author's research and associated work as it does. The difficulty is that it could well be regarded as too theoretical. The theorems (and lemmas) often involve highly abstract spaces and the proofs of some of them (not always following on their enunciation) involve six pages. In most cases the lead-in to numerical calculations could, I feel, be expanded. It is surprising that, in this day and age, rationalized MKS units are not used. The appearance of the book is pleasing, but there are some printing errors, e.g. page 25 ``further set \(\gamma=2\), and we further set \(\gamma_.=2\)'' and it would be more usual to print terms such as ``\(\log_3(1/h)\)'' as ``\(-\log_3h\)''.NEWLINENEWLINENEWLINEThis is a highly specialized work and the publishers are to be thanked for producing it at what is these days a reasonable price.