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 domain decomposition, or the artificial sub-sectioning technique, along with a region-by-region iteration algorithm particularly tailored for parallel computation to address the coefficient matrix issue is developed.
Abstract: Mesh reduction methods such as boundary element methods, method of fundamental solutions, and spectral methods all lead to fully populated matrices. This poses serious challenges for large-scale three-dimensional problems due to storage requirements and iterative solution of a large set of non-symmetric equations. Researchers have developed several approaches to address this issue including the class of fast-multipole techniques, use of wavelet transforms, and matrix decomposition. In this paper, we develop a domain decomposition, or the artificial sub-sectioning technique, along with a region-by-region iteration algorithm particularly tailored for parallel computation to address the coefficient matrix issue. The meshless method we employ is based on expansions using radial-basis functions (RBFs). An efficient physically based procedure provides an effective initial guess of the temperatures along the sub-domain interfaces. The iteration process converges very efficiently, offers substantial savings in memory, and features superior computational efficiency. The meshless iterative domain decomposition technique is ideally suited for parallel computation. We discuss its implementation under MPI standards on a small Windows XP PC cluster. Numerical results reveal the domain decomposition meshless methods produce accurate temperature predictions while requiring a much-reduced effort in problem preparation in comparison to other traditional numerical methods.
57 citations
TL;DR: In this paper, an edge-based smoothed finite element method (ES-FEM) is formulated for stress field determination of elasticplastic problems using triangular meshes, in which smoothing domains associated with the edges of the triangles are used for smoothing operations to improve the accuracy and the convergence rate of the method.
56 citations
TL;DR: In this paper, the International journal for numerical methods in engineering, el 08/06/2005, the authors present an abstract of their paper, entitled "A Mathematical Approach for numerical Methods in Engineering".
Abstract: Aceptado para su publicacion en International journal for numerical methods in engineering, el 08/06/2005
56 citations
TL;DR: The local discontinuous Galerkin and variational multiscale EFG methods are applied for obtaining numerical solution of two-dimensional Brusselator system with and without cross-diffusion.
56 citations
TL;DR: In this article, two computational models, Simulating WAVE till SHore (SWASH) and DualSPHysics, with different computational costs and capabilities have been hybridized in this work.
Abstract: Two computational models, Simulating WAve till SHore (SWASH) and DualSPHysics, with different computational costs and capabilities have been hybridized in this work. SWASH is a time-domain wave mod...
56 citations