Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.

Non‐linear dynamic analyses by meshless local Petrov–Galerkin formulations

Abstract: In this work, meshless methods based on the local Petrov–Galerkin approach are proposed for the solution of dynamic problems considering elastic and elastoplastic materials. Formulations adopting the Heaviside step function and the Gaussian weight function as the test functions in the local weak form are considered. The moving least-square method is used for the approximation of physical quantities in the local integral equations. After spatial discretization is carried out, a non-linear system of ordinary differential equations of second order is obtained. This system is solved by Newmark/Newton–Raphson techniques. At the end of the paper numerical results are presented, illustrating the potentialities of the proposed methodologies. Copyright © 2009 John Wiley & Sons, Ltd.

Meshfree representation and computation: applications to cardiac motion analysis.

Abstract: For medical image analysis issues where the domain mappings between images involve large geometrical shape changes, such as the cases of nonrigid motion recovery and inter-object image registration, the finite element methods exhibit considerable loss of accuracy when the elements in the mesh become extremely skewed or compressed. Therefore, algorithmically difficult and computationally expensive remeshing procedures must be performed in order to alleviate the problem. We present a general representation and computation framework which is purely based on the sampling nodal points and does not require the construction of mesh structure of the analysis domain. This meshfree strategy can more naturally handle very large object deformation and domain discontinuity problems. Because of its intrinsic h-p adaptivity, the meshfree framework can achieve desired numerical accuracy through adaptive node and polynomial shape function refinement with minimum extra computational expense. We focus on one of the more robust meshfree efforts, the element free Galerkin method, through the moving least square approximation and the Galerkin weak form formulation, and demonstrate its relevancy to medical image analysis problems. Specifically, we show the results of applying this strategy to physically motivated multi-frame motion analysis, using synthetic data for accuracy assessment and for comparison to finite element results, and using canine magnetic resonance tagging and phase contrast images for cardiac kinematics recovery.

Coupled Radiation and Mixed Convection in an Eccentric Annulus Using the Hybrid Strategy of Lattice Boltzmann-Meshless Method

Abstract: A numerical investigation has been made of the interaction of thermal radiation with laminar mixed convection in an eccentric annulus filled with participating media. As a hybrid approach based on a common multiscale Boltzmann-type model, the combination of lattice Boltzmann and direct collocation meshless methods (LB-DCM) is developed to solve the coupled problem of radiation and convection. Numerical simulations are conducted for different eccentricities, Rayleigh number, Reynolds number, convection-radiation parameter, and optical thickness. Results show that the LB-DCM combination is stable and accurate. In addition, this hybrid approach is easy to implement and has excellent flexibility in dealing with irregular geometries.