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Handbook of Materials Modeling pp 2447–2474Cite as

Meshless Methods for Numerical Solution of Partial Differential Equations

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Abstract

A popular research topic in numerical methods recently has been the development of meshless methods as alternatives to the traditional finite element, finite volume, and finite difference methods. The traditional methods all require some connectivity knowledge a priori, such as the generation of a mesh, whereas the aim of meshless methods is to sprinkle only a set of points or nodes covering the computational domain, with no connectivity information required among the set of points. Multiphysics and multiscale analysis, which is a common requirement for microsystem technologies such as MEMS and Bio-MEMS, is radically simplified by meshless techniques as we deal with only nodes or points instead of a mesh. Meshless techniques are also appealing because of their potential in adaptive techniques, where a user can simply add more points in a particular region to obtain more accurate results.

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Authors and Affiliations

  1. Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana Champaign, Urbana, IL, 61801, USA

    Gang Li, Xiaozhong Jin & N. R. Alum

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  1. Gang Li
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  2. Xiaozhong Jin
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  3. N. R. Alum
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Editors and Affiliations

  1. Massachusetts Institute of Technology, USA

    Sidney Yip

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© 2005 Springer

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Li, G., Jin, X., Alum, N.R. (2005). Meshless Methods for Numerical Solution of Partial Differential Equations. In: Yip, S. (eds) Handbook of Materials Modeling. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3286-8_128

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