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solved examples on mesh free method

Submitted by muhammad asif rajput on

plz provide links for some solved numerical examples for new students in this field of mesh free method

Hi Muhammad,

The famous square plate with a circular hole in the center and crack problem are solved as benchmark problems in the MFree2D package developed by Liu and co-workers.  See the following site for download and examples.   

http://www.nus.edu.sg/ACES/software/meshless2D/webfiles/webpageMFree.ht…;

I'm sure in the literature you can find many boundary value problems solved using meshfree techniques.  One example in geomechanics is given by

Zhang et al, . A meshfree method and its applications to elastoplastic problems, J Zhejiang Univ SCI 2005 6A(2): 148-154  

If you're a developer and looking for a development code for meshfree Tahoe(Sandia National Lab research code that includes finite element, particle and meshfree methods) is one of the available codes.  Some benchmark problems are solved.  See

http://tahoe.cvs.sourceforge.net/tahoe/benchmark_XML/level.0/meshfree/

I hope this helps a bit.  I'm sure other meshfree folks can be of more help than me.

Good luck exploring the meshfree world!

Karma 

 

Mon, 07/02/2007 - 17:21 Permalink

hi

the link you have provided it is not working. give some other references such that we can get some solved examples of mesh free .

 

thank you 

Sat, 08/11/2007 - 18:04 Permalink

I think that the previous comments highlight the difficulties involved in learing a new method, without access to a knowledgeable person/expert in that particular method.

 I think that there is a need for a book (maybe even open source book), that deals with numerical methods in one dimension, without being rigorous. The target reader of this book would be someone who has a basic  knowledge  (1 graduate course) of finite differences or finite elements.

 For example, to solve a P.D.E., there is finite differences, finite elements, stabilized finite elements, multiscale finite elements, adaptive (hp) finite eleemnt methods, meshless methods (Element free Galerkin, Finite Spheres, Local Petrov Galerkin (?),), Material Point Method, and many many more. Each of these methods has its own advantages / disadvantages, with no real silver bullet. 

 If one is not devoted to full time research on these methods, it is hard to find the itme to read and understand the original papers.  It would be very nice to have something of this sort: a recipe book, if you will for the solution of P.D.E.'s Something along the lines of Jack Dongarra's book  Templates for the Solution of Linear System would be very nice.

Perhaps this could be a collaboration project for imechanica readers: We could all edit a single common LaTeX file and create such a template, not more than 50 pages with, approximately 2 pages per numerical mathod.   

 -Amit  

Sat, 08/11/2007 - 18:37 Permalink