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Advances in Trefftz methods and thei...

Alves, Carlos.

Advances in Trefftz methods and their applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Advances in Trefftz methods and their applicationsedited by Carlos Alves ... [et al.].
other author:	Alves, Carlos.
Published:	Cham :Springer International Publishing :2020.
Description:	xiv, 203 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Differential equations, Partial.
Online resource:	https://doi.org/10.1007/978-3-030-52804-1
ISBN:	9783030528041$q(electronic bk.)

Advances in Trefftz methods and their applications
Advances in Trefftz methods and their applications[electronic resource] /edited by Carlos Alves ... [et al.]. - Cham :Springer International Publishing :2020. - xiv, 203 p. :ill., digital ;24 cm. - SEMA SIMAI Springer series,v.232199-3041 ;. - SEMA SIMAI Springer series ;v.4..

1 Chen, M. et al., Solving Partial Diﬀerential Equations on Surfaces with Fundamental Solutions -- 2 Akhmouch, L. et al., Solving magneto-hydrodynamic (MHD) channel ﬂows at large Hartmann numbers by using the method of fundamental solutions -- 3 Gaspar, C. et al., Application of Quadtrees in the Method of Fundamental Solutions using Multi-Level Tools -- 4 Liu, Q., Method of Fundamental Solutions without Fictitious Boundary for Anisotropic Elasticity Problems Based on Mechanical Equilibrium Desingularization -- 5 Barbeiro, S. and Serranho, P., The method of fundamental solutions for the direct elastography problem in the human retina -- 6 Martins, Nuno F. M., Identiﬁcation and reconstruction of body forces in a Stokes system using shear waves -- 7 Marin, L., MFS-Fading Regularization Method for Inverse BVPs in Anisotropic Heat Conduction -- 8. Mocerino, A., et al., Non-intrusive Estimate of Spatially Varying Internal Heat Flux in Coiled Ducts: Method of Fundamental Solutions Applied to the Reciprocity Functional Approach -- 9 Moldovan, D.I., et al., Uniﬁed hybrid-Treﬀtz ﬁnite element formulation for dynamic problems -- 10. Fu, Z.-J. et al., Acoustic bandgap calculation of liquid phononic crystals via the meshless generalized ﬁnite diﬀerence method.

In this book we gather recent mathematical developments and engineering applications of Trefftz methods, with particular emphasis on the Method of Fundamental Solutions (MFS) These are true meshless methods that have the advantage of avoiding the need to set up a mesh altogether, and therefore going beyond the reduction of the mesh to a boundary. These Trefftz methods have advantages in several engineering applications, for instance in inverse problems where the domain is unknown and some numerical methods would require a remeshing approach. Trefftz methods are also known to perform very well with regular domains and regular data in boundary value problems, achieving exponential convergence. On the other hand, they may also under certain conditions, exhibit instabilities and lead to ill-conditioned systems. This book is divided into ten chapters that illustrate recent advances in Trefftz methods and their application to engineering problems. The first eight chapters are devoted to the MFS and variants whereas the last two chapters are devoted to related meshless engineering applications. Part of these selected contributions were presented in the 9th International Conference on Trefftz Methods and 5th International Conference on the MFS, held in 2019, July 29-31, in Lisbon, Portugal.

ISBN: 9783030528041$q(electronic bk.)

Standard No.: 10.1007/978-3-030-52804-1doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA371 / .A38 2020

Dewey Class. No.: 515.353

Advances in Trefftz methods and their applications
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505 0 $a 1 Chen, M. et al., Solving Partial Diﬀerential Equations on Surfaces with Fundamental Solutions -- 2 Akhmouch, L. et al., Solving magneto-hydrodynamic (MHD) channel ﬂows at large Hartmann numbers by using the method of fundamental solutions -- 3 Gaspar, C. et al., Application of Quadtrees in the Method of Fundamental Solutions using Multi-Level Tools -- 4 Liu, Q., Method of Fundamental Solutions without Fictitious Boundary for Anisotropic Elasticity Problems Based on Mechanical Equilibrium Desingularization -- 5 Barbeiro, S. and Serranho, P., The method of fundamental solutions for the direct elastography problem in the human retina -- 6 Martins, Nuno F. M., Identiﬁcation and reconstruction of body forces in a Stokes system using shear waves -- 7 Marin, L., MFS-Fading Regularization Method for Inverse BVPs in Anisotropic Heat Conduction -- 8. Mocerino, A., et al., Non-intrusive Estimate of Spatially Varying Internal Heat Flux in Coiled Ducts: Method of Fundamental Solutions Applied to the Reciprocity Functional Approach -- 9 Moldovan, D.I., et al., Uniﬁed hybrid-Treﬀtz ﬁnite element formulation for dynamic problems -- 10. Fu, Z.-J. et al., Acoustic bandgap calculation of liquid phononic crystals via the meshless generalized ﬁnite diﬀerence method.
520 $a In this book we gather recent mathematical developments and engineering applications of Trefftz methods, with particular emphasis on the Method of Fundamental Solutions (MFS) These are true meshless methods that have the advantage of avoiding the need to set up a mesh altogether, and therefore going beyond the reduction of the mesh to a boundary. These Trefftz methods have advantages in several engineering applications, for instance in inverse problems where the domain is unknown and some numerical methods would require a remeshing approach. Trefftz methods are also known to perform very well with regular domains and regular data in boundary value problems, achieving exponential convergence. On the other hand, they may also under certain conditions, exhibit instabilities and lead to ill-conditioned systems. This book is divided into ten chapters that illustrate recent advances in Trefftz methods and their application to engineering problems. The first eight chapters are devoted to the MFS and variants whereas the last two chapters are devoted to related meshless engineering applications. Part of these selected contributions were presented in the 9th International Conference on Trefftz Methods and 5th International Conference on the MFS, held in 2019, July 29-31, in Lisbon, Portugal.
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