This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics.
The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications.
This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.
The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications.
This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.
From the reviews:
"The main goal of this book is to explain the mathematical foundation of the boundary element methods (BEMs) ... . The BEM is well developed and widely used by engineers and scientists in applied mathematical computations for 40 years. ... The book will be helpful not only for mathematicians who want to become familiar with the BIE but also for users of BEMs who want to understand mathematical background of the computational method." (Vladimir Sládek, Zentralblatt MATH, Vol. 1157, 2009)
"This book has been in preparation for many years: the care in its composition is evident. ... The development of ... analytical framework occupies the major part of this impressive book. ... There are 10 chapters and a bibliography of 325 items. ... In summary, this is an important scholarly work on the modern mathematical theory of boundary integral equations." (Paul Andrew Martin, Mathematical Reviews, Issue 2009 i)
"The main goal of this book is to explain the mathematical foundation of the boundary element methods (BEMs) ... . The BEM is well developed and widely used by engineers and scientists in applied mathematical computations for 40 years. ... The book will be helpful not only for mathematicians who want to become familiar with the BIE but also for users of BEMs who want to understand mathematical background of the computational method." (Vladimir Sládek, Zentralblatt MATH, Vol. 1157, 2009)
"This book has been in preparation for many years: the care in its composition is evident. ... The development of ... analytical framework occupies the major part of this impressive book. ... There are 10 chapters and a bibliography of 325 items. ... In summary, this is an important scholarly work on the modern mathematical theory of boundary integral equations." (Paul Andrew Martin, Mathematical Reviews, Issue 2009 i)