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Advances in Trefftz methods and their applications. Selected papers based on the presentations at the 9th conference on Trefftz methods and 5th conference on method of fundamental solutions, Lisbon, Portugal, July 29–31, 2019. (English) Zbl 1445.65001

SEMA SIMAI Springer Series 23. Cham: Springer (ISBN 978-3-030-52803-4/hbk; 978-3-030-52806-5/pbk; 978-3-030-52804-1/ebook). xiv, 203 p. (2020).

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Publisher’s description: 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.
The articles of this volume will be reviewed individually.
Indexed articles:
Chen, Meng; Cheung, Ka Chun; Ling, Leevan, Solving partial differential equations on surfaces with fundamental solutions, 1-11 [Zbl 1454.65183]
Akhmouch, Latifa; Naji, Ahmed; Duan, Yong; Fu, Zhuojia, Solving magneto-hydrodynamic (MHD) channel flows at large Hartmann numbers by using the method of fundamental solutions, 13-40 [Zbl 1454.65181]
Gáspár, Csaba, Application of quadtrees in the method of fundamental solutions using multi-level tools, 41-57 [Zbl 1453.65432]
Liu, Qingguo; Šarler, Božidar, Method of fundamental solutions without fictitious boundary for anisotropic elasticity problems based on mechanical equilibrium desingularization, 59-86 [Zbl 1453.65433]
Barbeiro, Sílvia; Serranho, Pedro, The method of fundamental solutions for the direct elastography problem in the human retina, 87-101 [Zbl 1454.65182]
Martins, Nuno F. M., Identification and reconstruction of body forces in a Stokes system using shear waves, 103-120 [Zbl 1452.65213]
Marin, Liviu, MFS-fading regularization method for inverse BVPs in anisotropic heat conduction, 121-138 [Zbl 1452.65212]
Mocerino, Andrea; Bozzoli, Fabio; Cattani, Luca; Vocale, Pamela; Rainieri, Sara, Non-intrusive estimate of spatially varying internal heat flux in coiled ducts: method of fundamental solutions applied to the reciprocity functional approach, 139-155 [Zbl 1452.65389]
Moldovan, Ionuţ Dragoş; Cismaşiu, Ildi; De Freitas, João António Teixeira, Unified hybrid-Trefftz finite element formulation for dynamic problems, 157-188 [Zbl 1451.65151]
Fu, Zhuo-Jia; Li, Ai-Lun; Zhang, Han, Acoustic bandgap calculation of liquid phononic crystals via the meshless generalized finite difference method, 189-203 [Zbl 1451.65170]

MSC:

65-06 Proceedings, conferences, collections, etc. pertaining to numerical analysis
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65Nxx Numerical methods for partial differential equations, boundary value problems
74Sxx Numerical and other methods in solid mechanics
76Mxx Basic methods in fluid mechanics
00B25 Proceedings of conferences of miscellaneous specific interest
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