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Local integration of 2-D fractional telegraph equation via local radial point interpolant approximation

In this article, a general type of two-dimensional time-fractional telegraph equation explained by the Caputo derivative sense for (1 < α ≤ 2) is considered and analyzed by a method based on the Galerkin weak form and local radial point interpolant (LRPI) approximation subject to given appropriate initial and Dirichlet boundary conditions.

interpolation/approximation method for accurate evaluation of higher order derivatives of shape functions


I  want to solve some problem from solid mechanics by means of meshless methods. Do you know some interpolation/approximation method which is able to accurate evaluate 3rd and 4th derivations of the shape functions and is not difficult to implement? MLS or PIM have problem with accuracy in these derivatives, as is known.
Thank you very much for your advices.

Ettore Barbieri's picture

DPhil Studentship at University of Oxford - funded by Rolls-Royce

Dear All,

we have a DPhil studentship available in the Solid Mechanics and Materials Engineering Group, within the Impact Engineering Laboratory led by Prof Nik Petrinic.

Questions about RPIM shapefunction

I am solving a simple solid mechanics problem by meshless method.  use RPIM to  calculate shape function.

when i calculate the derivatives of shape function, i found the derivative is not close to zero at the compute point, when the point is on the boundry of problem domain. and good derivative result can be got if the compute point is in problem domain. 

is there anybody has experience in working with RPIM shape function help me to fix the problem? 


Question about how to determine support radius..

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Hi, everyone.

I'm going to employ the meshfree method to analyze composite model.

But, I can't understand how to determine the support radius although I have read some references.

I will use the circular support domain.

Please explain how to determine the support radius.

Definition of Reproducing Kernel

Hi all, I am currently beginning research as a graduate student on meshfree methods, focusing on RKPM right now. I have not been able to find an exact definition of what exactly a reproducing kernel means. Could someone kindly define a reproducing kernel? According to W.K Liu et al, a good example of a reproducing kernel is a Fourier transform, but I can't grasp why is that so.

CMMSE 2010 - Call for papers - Minisymposium on Sampling theory and meshfree methods

Please note the Minisymposium on Sampling theory and meshfree methods as a part of

the International Conference on Computational and Mathematical methods in Science and Engineering
CMMSE 2010, 26-30 June 2010, Almeria, Andalucia, Spain
--  --

 This mini-symposium aims to bring together such related areas of
mathematics and computational mechanics as Sampling Theory and Meshfree
Numerical Methods.

Problems with MLPG and collocation

I fight with my models... Maybe can somebody of us help me...

I model the three dimensional body, those two sizes length and width are much larger then the thickness. For solving PDE i use MLPG Method. After defining my hexahedral support domain with MLS and hexahedral test doman with Heaviside function, i make the nodal integration. For that i divide the hole problem in hexahedrals, in the centers of those the particles are placed. Then i compute the surface of the hexahedrals in test domain through gauss quadratur to assemble the stiffness matrix 

Volume integration in mehsless methods

I use the meshless Galerkin method for 3D simulation of plate movement. This method requires the volume integration over a test domain. Could somebody help me with the volume integration? I wonder if there are standard or open source algorithms that can be used for this problem.

I would appriciate any help.

second derivative of MLS function

Can somebody help me with the second derivative of MLS function for three dimentional problems?

Ettore Barbieri's picture

The Future of Meshless Methods

I joined imechanica almost a year ago and I've been frequently following its interesting discussions, even the most animated ones. I think that a place like this is ideal to foster the exchange of ideas in the scientific community;

Moreover it is fantastic as a simple student like me can interact and easily ask questions to the most important researcher in the field of mechanics.

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