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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01 Jan 2004
TL;DR: Mesh free methods do not requires ophisticated algorithms and data structures for maintaining a grid, which is often the most time consuming task in mesh-based simulations.
Abstract: Mesh free methods are recent and modern discretization techniques for numerically solving partial differentialequations(PDEs). In contrast to the well-established traditional methods, such asfinite differences(FD),finite volumes(FV), and finite element methods(FEM), mesh free methods do not requires ophisticated algorithms and data structures for maintaining a grid, which is often the most time consuming task in mesh-based simulations.
1 citations
TL;DR: In this article, an efficient mesh-free method based on a stabilized conforming nodal integration method is developed for elastoplastic contact analysis of metal forming processes, where strain smoothing stabilization is introduced to eliminate spatial instability in Galerkin mesh free methods.
Abstract: An efficient meshfree method based on a stabilized conforming nodal integration method is developed for elastoplastic contact analysis of metal forming processes. In this approach, strain smoothing stabilization is introduced to eliminate spatial instability in Galerkin meshfree methods when the weak form is integrated by a nodal integration. The gradient matrix associated with strain smoothing satisfies the integration constraint for linear exactness in the Galerkin approximation. Strain smoothing formulation and numerical procedures for path-dependent problems are introduced. Applications of metal forming analysis are presented, from which the computational efficiency has been improved significantly without loss of accuracy.
1 citations
TL;DR: This paper applies the localized method of particular solutions and the closed-form particular solution to simplify the two-stage approach using Chebyshev polynomial as the basis functions for solving axisymmetric problems and proposes the modified local Pascal polynometric method (MLPM).
1 citations
09 May 2010
TL;DR: In this paper, a technique for combination of fast moving least square reproducing kernel method (FMLSRKM) which is a kind of mesh free methods and finite element method (FEM) is used.
Abstract: In this paper, a technique for combination of fast moving least square reproducing kernel method (FMLSRKM) which is a kind of meshfree methods and finite element method (FEM). Point collocation scheme is used for FMSLRKM. Combined method is tested using 2D electrostatic problem.
1 citations
01 Jan 2011
TL;DR: In this article, the divergence-free interpolation problem is converted to a generalized Stokes problem, and an Uzawa-type method and the method of fundamental solutions are proposed to numerically solve this new problem.
Abstract: A vectorial interpolation problem is considered. In addition to the interpolation conditions taken at discrete points, a global, divergence-free condition is also prescribed. Utilizing the idea of the multi-elliptic interpolation, the divergencefree interpolation problem is converted to a generalized Stokes problem. To numerically solve this new problem, an Uzawa-type method and the method of fundamental solutions are proposed. In the second method, a linear system with large and dense matrix is to be solved, while in the first method, this problem is avoided.
1 citations