A truly meshless Galerkin method is formulated in the present study, as a special case of the general Meshless Local Petrov-Galerkin (MLPG) “Mixed” approach. The Galerkin method is implemented as a truly meshless method, for solving elasto-static problems. In the present Galerkin method, the test function is chosen to be the same as the trial function, as a special case of the MLPG approach. Ho...

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously nonhomogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The analyzed domain is covered by small subdomains with a simple geometry. A weak formulation for ...

In this paper, the meshless integral method based on the regularized boundary integral equation [1] has been extended to analyze the large deformation of elastoplastic materials. The updated Lagrangian governing integral equation is obtained from the weak form of elastoplasticity based on Green-Naghdi’s theory over a local sub-domain, and the moving least-squares approximation is used for meshl...

We propose a novel algorithm for modeling interface motions. The interface is represented and is tracked using quasi-uniform meshless particles. These particles are sampled according to an underlying grid such that each particle is associated to a grid point which is in the neighborhood of the interface. The underlying grid provides an Eulerian reference and local sampling rate for particles on...

A meshless local Petrov-Galerkin (MLPG) method is applied to solve problems of Reissner-Mindlin shells under thermal loading. Both stationary and thermal shock loads are analyzed here. Functionally graded materials with a continuous variation of properties in the shell thickness direction are considered here. A weak formulation for the set of governing equations in the Reissner-Mindlin theory i...

Computational models of cardiac electrophysiology are promising tools for reducing the rates non-response patients suitable resynchronization therapy (CRT) by optimizing electrode placement. The majority computational in literature mesh-based, primarily using finite element method (FEM). generation patient-specific meshes has traditionally been a tedious task requiring manual intervention and h...

A localized radial basis function (RBF) meshless method is developed for coupled viscous fluid flow and convective heat transfer problems. The method is based on new localized radial-basis function (RBF) expansions using Hardy Multiquadrics for the sought-after unknowns. An efficient set of formulae are derived to compute the RBF interpolation in terms of vector products thus providing a substa...

We present a new approach to simultaneously denoise and parameterize unorganized point cloud data. This is achieved by minimizing an appropriate energy function defined on the point cloud and its parameterization. An iterative algorithm to minimize the energy is described. The key ingredient of our approach is an “as-rigid-as-possible” meshless parameterization to map a point cloud with disk to...