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The isogeometric boundary element method

Beer, Gernot.

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The isogeometric boundary element method

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The isogeometric boundary element method/ by Gernot Beer, Benjamin Marussig, Christian Duenser.
作者:	Beer, Gernot.
其他作者:	Marussig, Benjamin.
出版者:	Cham :Springer International Publishing : : 2020.,
面頁冊數:	xiv, 335 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer eBooks
標題:	Boundary element methods. -
電子資源:	https://doi.org/10.1007/978-3-030-23339-6
ISBN:	9783030233396

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.90..

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

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

566490
Boundary element methods.

LC Class. No.: TA347.B69

Dewey Class. No.: 515.35

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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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