Advanced Boundary Element Methods
Treatment of Boundary Value, Transmission and Contact Problems
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Beschreibung
This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods – efficient computational tools that have become extremely popular in applications.
Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research.
The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.
This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods – efficient computational tools that have become extremely popular in applications.
Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research.
The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.
Features fundamental chapters on boundary integral equations and their approximations by boundary elements to enable novice readers to become acquainted with a modern field of numerical analysis Discusses advanced key topics in BEM and presents the necessary tools of mathematical analysis, guiding readers to the forefront of reseach Describes numerous numerical experiments to help BEM practitioners in engineering and science understand modern, efficient and reliable versions of BEM
Autor*in
Joachim Gwinner
Themen in »Advanced Boundary Element Methods«
boundary integral equations boundary element Galerkin and collocation methods contact problems adaptive boundary elements time-domain boundary elements coupling of finite and boundary elements partial differential equations
Stimmen zu »Advanced Boundary Element Methods«
“The book can be recommended to researches in the field of mathematics and engineering and to graduate students to familiarize themselves with the state-of-the-art of boundary element methods.” (Dana Černá, zbMATH 1429.65001, 2020)
“The book can be recommended as a comprehensive set of results for the state of the art in BEM, and in the applications considered by the authors.” (Michael J. Carley, Mathematical Reviews, August, 2019)
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