Containing the latest in a long line of conferences covering the most recent advances in Boundary Elements and Mesh Reduction Methods (BEM/MRM), this book contains an important chapter in the history of this important method used in science and engineering. The BEM/MRM conference has long been recognised as THE international forum on the technique. The proceedings of the conference therefore constitute a record of the development of the method, running from the initial successful development of boundary integral techniques into the BEM, a method that eliminates the need for an internal mesh, to the recent and most sophisticated Mesh Reduction and even Meshless Methods. Since the boundary elements, mesh reduction, and meshless methods are used in many engineering and scientific fields, the book will be of great interest to all engineers and scientists working within the areas of numerical analysis, boundary elements and meshless methods. Topics covered include: Advanced formulations; Advanced meshless and mesh reduction methods; Structural mechanics applications; Solid mechanics; Heat and mass transfer, Electrical engineering and electromagnetics; Computational methods; Fluid flow modelling; Damage mechanics and fracture; Dynamics and Vibrations Engineering applications.

Boundary Elements and Other Mesh Reduction Methods XXXVIII (Wit Transactions on Modelling and Simulation)

Science & Math

A. H.-D. Cheng

Mathematics

Wit Press/Computational Mechanics

This book covers a class of numerical methods that are generally referred to as "Collocation Methods". Different from the Finite Element and the Finite Difference Method, the discretization and approximation of the collocation method is based on a set of unstructured points in space. This "meshless" feature is attractive because it eliminates the bookkeeping requirements of the "element" based methods. This text discusses several types of collocation methods including the radial basis function method, the Trefftz method, the Schwartz alternating method, and the couple collocation and finite element method. Governing equations investigated include Laplace, Poisson, Helmholtz and bioharmonic equations. Regular boundary value problems, boundary value problems with singularity and eigenvalue problems are also examined, Rigorous mathematical proofs are contained in these chapters, and many numerical experiments are also provided to support the algorithms and to verify the theory. A tutorial on the applications of these methods is also provided.

Trefftz and Collocation Methods

Z.-C. Li

T.-T. Lu

H-Y. Hu

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Books by A. H.-D. Cheng