Meshfree methods

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

A method for terminating mesh lines in finite difference formulations of the semiconductor device equations

Abstract: In this paper a method is described for terminating mesh lines in one or two dimensions within the context of the finite difference formulation of the semiconductor device equations This saves both computer time and storage since unneeded mesh points are eliminated. However, more importantly it can result in a system of equations that are better conditioned in the case of devices where the coupling between portions of the device is poor in the numerical sense. Several examples are shown of field effect power devices where convergence was only possible after the line termination methods were applied. Finally, a short discussion is presented on the relative advantages of the finite difference formalism in comparison to the finite element methods in light of the line termination technique.

Implementation of a generalized exponential basis functions method for linear and non‐linear problems

Abstract: This is the accepted version of the following article: Mossaiby, F., Ghaderian, M., Rossi, R. Implementation of a generalized exponential basis functions method for linear and non-linear problems. International Journal for Numerical Methods in Engineering [on line]. Jul 2015, which has been published in final form at http://dx.doi.org/10.1002/nme.4985.

Semi-Lagrangian reproducing kernel particle method for slope stability analysis and post-failure simulation

Abstract: Slope stability analyses are often performed using Limit Equilibrium Methods (LEMs) and Finite Element Method (FEM). However, these methods can only model the slope condition up to the point of failure. Meshfree methods, which do not require a mesh or a grid in the simulation process, have the potential to model the post-failure slope behavior as mesh tangling would not occur to cause numerical instability and non-convergence. Hence, while retaining the benefits of conventional numerical schemes, meshfree method can be more advantageous when problems with large deformation are encountered. In this paper, Semi-Lagrangian Reproducing Kernel Particle Method (SLRKPM), which is a type of meshfree method, is extended to analyze geomechanics problems such as the stability of a slope and post failure slope behavior. The results from SLRKPM agree well with those from convention methods (LEMs and FEM) in terms of factor-of-safety and failure surface. In addition, SLRKPM is able to simulate the slope failure process and successfully capture the development of shear band. This proves that SLRKPM has a significant advantage over FEM when dealing with problems involving large deformation and failure of geomaterials.

Particle-based and Meshless Methods with Aboria

Abstract: Aboria is a powerful and flexible C++ library for the implementation of particle-based numerical methods. The particles in such methods can represent actual particles (e.g. Molecular Dynamics) or abstract particles used to discretise a continuous function over a domain (e.g. Radial Basis Functions). Aboria provides a particle container, compatible with the Standard Template Library, spatial search data structures, and a Domain Specific Language to specify non-linear operators on the particle set. This paper gives an overview of Aboria's design, an example of use, and a performance benchmark.