✍ Scribed by Carlos Alves, Andreas Karageorghis, Vitor Leitão, Svilen Valtchev
No coin nor oath required. For personal study only.
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.
Front Matter ....Pages i-xiv
Solving Partial Differential Equations on Surfaces with Fundamental Solutions (Meng Chen, Ka Chun Cheung, Leevan Ling)....Pages 1-11
Solving Magneto-Hydrodynamic (MHD) Channel Flows at Large Hartmann Numbers by Using the Method of Fundamental Solutions (Latifa Akhmouch, Ahmed Naji, Yong Duan, Zhuojia Fu)....Pages 13-40
Application of Quadtrees in the Method of Fundamental Solutions Using Multi-Level Tools (Csaba Gáspár)....Pages 41-57
Method of Fundamental Solutions Without Fictitious Boundary for Anisotropic Elasticity Problems Based on Mechanical Equilibrium Desingularization (Qingguo Liu, Božidar àarler)....Pages 59-86
The Method of Fundamental Solutions for the Direct Elastography Problem in the Human Retina (Sílvia Barbeiro, Pedro Serranho)....Pages 87-101
Identification and Reconstruction of Body Forces in a Stokes System Using Shear Waves (Nuno F. M. Martins)....Pages 103-120
MFS-Fading Regularization Method for Inverse BVPs in Anisotropic Heat Conduction (Liviu Marin)....Pages 121-138
Non-intrusive Estimate of Spatially Varying Internal Heat Flux in Coiled Ducts: Method of Fundamental Solutions Applied to the Reciprocity Functional Approach (Andrea Mocerino, Fabio Bozzoli, Luca Cattani, Pamela Vocale, Sara Rainieri)....Pages 139-155
Unified Hybrid-Trefftz Finite Element Formulation for Dynamic Problems (Ionuţ Dragoş Moldovan, Ildi Cismaşiu, João António Teixeira de Freitas)....Pages 157-188
Acoustic Bandgap Calculation of Liquid Phononic Crystals via the Meshless Generalized Finite Difference Method (Zhuo-Jia Fu, Ai-Lun Li, Han Zhang)....Pages 189-203
Mathematics; Computational Mathematics and Numerical Analysis; Computer Science, general; Theoretical, Mathematical and Computational Physics
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