G. R. Liu, Y. T. Gu ... 480 pages - Publisher: Springer; (July, 2005) ...
Language: English - ISBN-10: 1402032285 - ISBN-13: 978-1402032288 ...
The finite difference method (FDM) hasbeen used tosolve differential
equation systems for centuries. The FDM works well for problems of
simple geometry and was widely used before the invention of the much
more efficient, robust finite element method (FEM). FEM is now widely
used in handling problems with complex geometry. Currently, we are using
and developing even more powerful numerical techniques aiming to obtain
more accurate approximate solutions in a more convenient manner for
even more complex systems. The meshfree or meshless method is one such
phenomenal development in the past decade, and is the subject of this
book. There are many MFree methods proposed so far for different
applications. Currently, three monographs on MFree methods have been
published. Mesh Free Methods, Moving Beyond the Finite Element Method d
by GR Liu (2002) provides a systematic discussion on basic theories,
fundamentals for MFree methods, especially on MFree weak-form methods.
It provides a comprehensive record of well-known MFree methods and the
wide coverage of applications of MFree methods to problems of solids
mechanics (solids, beams, plates, shells, etc.) as well as fluid
mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri
and Shen (2002) provides detailed discussions of the meshfree local
Petrov-Galerkin (MLPG) method and itsvariations. Formulations and
applications of MLPG are well addressed in their book.