Meshfree Methods for Partial Differential Equations VIII

There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods have a number of advantageous features that are especially attractive when dealing with multiscale phenomena: A-priori knowledge about the solution's particular local behavior can easily be introduced into the meshfree approximation space, and coarse scale approximations can be seamlessly refined by adding fine scale information. However, the implementation of meshfree methods and their parallelization also requires special attention, for instance with respect to numerical integration.

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Summary

There have been substantial developments in meshfree methods, particle methods, and generalized finite element methods since the mid 1990s. The growing interest in these methods is in part due to the fact that they offer extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods have a number of advantageous features that are especially attractive when dealing with multiscale phenomena: A-priori knowledge about the solution’s particular local behavior can easily be introduced into the meshfree approximation space, and coarse scale approximations can be seamlessly refined by adding fine scale information. However, the implementation of meshfree methods and their parallelization also requires special attention, for instance with respect to numerical integration.

Product details

• Assisted by: Alexander Schweitzer (Editor), Alexander Schweitzer (Editor), Michae Griebel (Editor), Michael Griebel (Editor), Marc Alexander Schweitzer (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2018
• EAN: 9783319847870
• ISBN: 978-3-31-984787-0
• No. of pages: 240
• Dimensions: 155 mm x 13 mm x 235 mm
• Weight: 385 g
• Illustrations: VIII, 240 p. 69 illus., 58 illus. in color.
• Series: Lecture Notes in Computational Science and Engineering; Lecture Notes in Computational Science and Engineering
• Subjects: Natural sciences, medicine, IT, technology > IT, data processing > General, dictionaries; C, Computer-Aided Design (CAD), computer science, Mathematics and Statistics, Mathematics of Computing, Computer mathematics, Numerical analysis, Mathematical theory of computation, Computational Science and Engineering, Maths for engineers, Mathematical modelling, Computer simulation, Computer modelling & simulation, Simulation and Modeling, Computer-Aided Engineering (CAD, CAE) and Design, Computer-aided engineering, Mathematical Modeling and Industrial Mathematics, Mathematical models, Numeric Computing