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The isogeometric boundary element method

Beer, Gernot.

The isogeometric boundary element method

Record Type:	Electronic resources : Monograph/item
Title/Author:	The isogeometric boundary element methodby Gernot Beer, Benjamin Marussig, Christian Duenser.
Author:	Beer, Gernot.
other author:	Marussig, Benjamin.
Published:	Cham :Springer International Publishing :2020.
Description:	xiv, 335 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Boundary element methods.
Online resource:	https://doi.org/10.1007/978-3-030-23339-6
ISBN:	9783030233396$q(electronic bk.)

The isogeometric boundary element method
Beer, Gernot.

The isogeometric boundary element method[electronic resource] /by Gernot Beer, Benjamin Marussig, Christian Duenser. - Cham :Springer International Publishing :2020. - xiv, 335 p. :ill., digital ;24 cm. - Lecture notes in applied and computational mechanics,v.901613-7736 ;. - Lecture notes in applied and computational mechanics ;v.61..

Introduction -- The boundary integral equation -- Basis functions, B-splines -- Description of the geometry -- Getting geometry information from CAD programs -- Numerical treatment of integral equations -- Numerical integration -- Steady state potential problems -- Static linear solid mechanics -- Body force effects -- Treatment of inhomogeneities/inclusions -- Material non-linear behaviour -- Applications in geomechanics -- Viscous flow problems -- Time dependent problems -- Summary and outlook -- Appendix A: Fundamental solutions.

This book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing.

ISBN: 9783030233396$q(electronic bk.)

Standard No.: 10.1007/978-3-030-23339-6doiSubjects--Topical Terms:

208685
Boundary element methods.

LC Class. No.: TA347.B69

Dewey Class. No.: 515.35

The isogeometric boundary element method
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245 1 4 $a The isogeometric boundary element method $h [electronic resource] / $c by Gernot Beer, Benjamin Marussig, Christian Duenser.
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300 $a xiv, 335 p. : $b ill., digital ; $c 24 cm.
490 1 $a Lecture notes in applied and computational mechanics, $x 1613-7736 ; $v v.90
505 0 $a Introduction -- The boundary integral equation -- Basis functions, B-splines -- Description of the geometry -- Getting geometry information from CAD programs -- Numerical treatment of integral equations -- Numerical integration -- Steady state potential problems -- Static linear solid mechanics -- Body force effects -- Treatment of inhomogeneities/inclusions -- Material non-linear behaviour -- Applications in geomechanics -- Viscous flow problems -- Time dependent problems -- Summary and outlook -- Appendix A: Fundamental solutions.
520 $a This book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing.
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