Topic
Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
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TL;DR: A numerical algorithm is described which gives a measure of the disorder in particle distributions in two and three dimensions, disregarding the fact they use topological connections between particles or not.
49 citations
TL;DR: In this paper, a mesh-free Galerkin (EFG) method is adopted for solving the governing partial differential equations of equilibrium and continuity of pore fluid flow for numerical simulation of coupled hydro-mechanical problems.
48 citations
01 Sep 2009
TL;DR: A mesh-free computational method based on radial basis functions in a finite difference mode (RBF-FD) has been developed for the incompressible Navier—Stokes equations in stream function vorticity form, and hence advancing solutions will in time be of comparatively lower cost.
Abstract: Meshless methods for solving fluid and fluid-structure problems have become a promising alternative to the finite volume and finite element methods. In this paper, a mesh-free computational method based on radial basis functions in a finite difference mode (RBF-FD) has been developed for the incompressible Navier—Stokes (NS) equations in stream function vorticity form. This compact RBF-FD formulation generates sparse coefficient matrices, and hence advancing solutions will in time be of comparatively lower cost. The spatial discretization of the incompressible NS equations is done using the RBF-FD method and the temporal discretization is achieved by explicit Euler time-stepping and the Crank—Nicholson method. A novel ghost node strategy is used to incorporate the no-slip boundary conditions. The performance of the RBF-FD scheme with the ghost node strategy is validated against a variety of benchmark problems, including a model fluid—structure interaction problem, and is found to be in a good agreement with the existing results. In addition, a higher-order RBF-FD scheme (which uses ideas from Hermite interpolation) is then proposed for solving the NS equations.
48 citations
01 May 1999
TL;DR: In this paper, the authors provide several answers to the issues: plain truncature of the balls, Lagrange multipliers technique, substitution method, and jump function for electromagnetic field analysis.
Abstract: When using meshless methods for electromagnetic field analysis, imposing boundary conditions and interface conditions are important sources of difficulties. This paper provides several answers to the issues: plain truncature of the balls; Lagrange multipliers technique; substitution method; and jump function. All those approaches are developed and compared.
48 citations
TL;DR: The generalized finite difference method (GFDM) is a mesh-free method that can be applied for solving problems defined over irregular clouds of points as discussed by the authors, which is used for solving elliptic and parabolic partial differential equations in 3D.
48 citations