LEADER 04797nam 22007095 450 001 9910483092503321 005 20251204102355.0 010 $a3-030-71127-7 024 7 $a10.1007/978-3-030-71127-6 035 $a(CKB)4100000011807068 035 $a(MiAaPQ)EBC6531799 035 $a(Au-PeEL)EBL6531799 035 $a(OCoLC)1245857973 035 $a(PPN)254719724 035 $a(BIP)79704141 035 $a(BIP)79056627 035 $a(DE-He213)978-3-030-71127-6 035 $a(EXLCZ)994100000011807068 100 $a20210326d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBoundary Integral Equations /$fby George C. Hsiao, Wolfgang L. Wendland 205 $a2nd ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (xx, 783 pages) $cillustrations 225 1 $aApplied Mathematical Sciences,$x2196-968X ;$v164 311 08$a3-030-71126-9 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Boundary Integral Equations -- Representation Formulae -- Sobolev Spaces -- Variational Formulations -- Electromagnetic Fields -- Introduction to Pseudodifferential Operators -- Pseudodifferential Operators as Integral Operators -- Pseudodifferential and Boundary Integral Operators -- Integral Equations on Recast as Pseudodifferential Equations -- Boundary Integral Equations on Curves in R^2. Remarks on Pseudodifferential Operators for Maxwell Equations -- Appendix A: Local Coordinates -- Appendix B: Vector Field Identities, Integration Formulae -- References -- Index. 330 $aThis is the second edition of the book which has two additional new chapters on Maxwell?s equations as well as a section on properties of solution spaces of Maxwell?s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell?s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering. 410 0$aApplied Mathematical Sciences,$x2196-968X ;$v164 606 $aMathematics$xData processing 606 $aNumerical analysis 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aMathematical analysis 606 $aComputational Mathematics and Numerical Analysis 606 $aNumerical Analysis 606 $aMathematical and Computational Engineering Applications 606 $aAnalysis 615 0$aMathematics$xData processing. 615 0$aNumerical analysis. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 0$aMathematical analysis. 615 14$aComputational Mathematics and Numerical Analysis. 615 24$aNumerical Analysis. 615 24$aMathematical and Computational Engineering Applications. 615 24$aAnalysis. 676 $a620.00151535 700 $aHsiao$b G. C$g(George C.),$0313294 702 $aWendland$b W. L$g(Wolfgang L.),$f1936- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483092503321 996 $aBoundary integral equations$92597295 997 $aUNINA