Table of Content

Open Access iconOpen Access

ARTICLE

Accurate MLPG Solution of 3D Potential Problems

Giorgio Pini1, Annamaria Mazzia1, Flavio Sartoretto2,

1 Dipartimento di Metodi eModelli Matematici per le ScienzeApplicate, Università di Padova, Italy, {pini,mazzia}@dmsa.unipd.it.
2 Dipartimento di Informatica Università di Venezia, Italy, sartoret@dsi.unive.it.

Computer Modeling in Engineering & Sciences 2008, 36(1), 43-64. https://doi.org/10.3970/cmes.2008.036.043

Abstract

Meshless methods have been explored in many 2D problems and they have been shown to be as accurate as Finite Element Methods (FEM). Compared to the extensive literature on 2D applications, papers on solving 3D problems by meshless methods are surprisingly few. Indeed, a main drawback of these methods is the requirement for accurate cubature rules. This paper focuses on the so called Meshless Local Petrov Galerkin (MLPG) methods. We show that accurate solutions of 3D potential problems can be attained, provided suitable cubature rules are identified, sparse data structures are efficiently stored, and strategies are devised in order to speed up the computation flow, by avoiding unnecessary integral evaluations. The ensuing MLPG linear systems result to be well conditioned, positive definite ones. Their conditioning does not increase much when the mesh size decreases. We show that cubature errors can lower MLPG convergence speed.

Keywords


Cite This Article

APA Style
Pini, G., Mazzia, A., Sartoretto, F., , (2008). Accurate MLPG solution of 3D potential problems. Computer Modeling in Engineering & Sciences, 36(1), 43-64. https://doi.org/10.3970/cmes.2008.036.043
Vancouver Style
Pini G, Mazzia A, Sartoretto F, . Accurate MLPG solution of 3D potential problems. Comput Model Eng Sci. 2008;36(1):43-64 https://doi.org/10.3970/cmes.2008.036.043
IEEE Style
G. Pini, A. Mazzia, F. Sartoretto, and , “Accurate MLPG Solution of 3D Potential Problems,” Comput. Model. Eng. Sci., vol. 36, no. 1, pp. 43-64, 2008. https://doi.org/10.3970/cmes.2008.036.043



cc Copyright © 2008 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
  • 1122

    View

  • 935

    Download

  • 0

    Like

Related articles

Share Link