The Meshless Local Petrov-Galerkin (MLPG) Method

By S. N.Atluri, S. Shen
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This book is the first monograph (in the new series, CREST), on this new class of meshless methods, that are expected to revolutionalize engineering/science analyses. It not only deals with several meshless methods in general, but also with the Meshhless Local Petrov-Galerkin (MLPG) method, pioneered by the authors, in particular.

Chapter Titles:

Chapter 1.

Global weak form and the weighted residual method (WRM); Point collocation method; Weighted integral square error; Subdomain integral/average error method; Finite volume method; Finite element method; Boundary element Method; Local weak forms;

Chapter 2.

Meshless interpolation of trial functions; Moving least-square approximation; Generalized moving least-square approximation; The influences of the weight function; Shepard functions;Partition of unity methods; Reproduced kernel particle method; Radial basis functions; Interpolation errors in meshless interpolations;

Chapter 3.

Meshless local Petrov-Galerkin method(MLPG); Numerical implementation of the MLPG; Six different Types of MLPG methods; Essential boundary conditions; Efficient Meshless Numerical integration; Numerical examples;Patch test,Laplace equation,Possion's equation; An analysis of the Computational costs; The nonlinear problem;

Chapter 4.

Application of MLPG in elasticity; The linear elasto-static problem;Arbitrary placement of secondary nodes, and error control; Elastostatic fracture; Analysis of beams using GMLS; Analysis of Shear-Flexible Beams & Shells;

Chapter 5.

Application of MLPG in fluid mechanics; The convection-diffusion problems; Berger's equations; Incompressible Navier-Stokes equations;

Chapter 6.

Prospects for future research: Nonlinear Analysis of Shells; Gradient Theories of inelasticity; Strain-localization; Nanotechnoloty.

Hardcover. 440 pages. © 2002. ISBN: 0-9657001-5-1.