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: The localized radial basis function collocation meshless method (LRBFCMM) is employed to solve time-depen... as discussed by the authors, which is also known as RBF-FD.
Abstract: The localized radial basis function collocation meshless method (LRBFCMM), also known as radial basis function generated finite differences (RBF-FD) meshless method, is employed to solve time-depen...
23 citations
TL;DR: The DVH method discussed in this work is characterized by the use of a regular distribution of points to perform the vorticity diffusion process, providing robustness and high accuracy of the method.
Abstract: In this paper two dimensional free vorticity dynamics is studied using two different particle methods. The first one is a Diffused Vortex Hydrodynamics (DVH) and the second one is a Smoothed Particle Hydrodynamics (SPH) method. These two methods present some similarities linked to their meshless nature but they are based on different numerical approaches. In this work advantages and drawbacks are highlighted by testing the particle methods on selected test-cases and by performing heuristic convergence measurements. The DVH method discussed in this work is characterized by the use of a regular distribution of points to perform the vorticity diffusion process. This redistribution avoids excessive clustering or rarefaction of the vortex particles providing robustness and high accuracy of the method.
23 citations
TL;DR: In this paper, a hybrid transform-based localized meshless method is constructed for the solution of fractional diffusion-wave equations and the time stepping procedure is avoided to overcome the problem of time in-stability related to meshless methods.
Abstract: In the present work, a hybrid transform-based localized meshless method is constructed for the solution of fractional diffusion-wave equations. The time stepping procedure is avoided to overcome the problem of time in-stability related to meshless methods. The issue of ill conditioning related to meshless differentiation matrices is resolved by incorporating small local system matrices. The time fractional diffusion-wave equation is selected to test the method. A clear improvement is observed in terms of stability, accuracy and ill-conditioning.
23 citations
TL;DR: In this article, the authors compared three methods for evaluating the domain integrals associated with the boundary element analysis of the three-dimensional Poisson and nonhomogeneous Helmholtz equations in complex multiply-connected geometries.
Abstract: The treatment of domain integrals has been a topic of interest almost since the inception of the boundary element method (BEM). Proponents of meshless methods such as the dual reciprocity method (DRM) and the multiple reciprocity method (MRM) have typically pointed out that these meshless methods obviate the need for an interior discretization. Hence, the DRM and MRM maintain one of the biggest advantages of the BEM, namely, the boundary-only discretization. On the other hand, other researchers maintain that classical domain integration with an interior discretization is more robust. However, the discretization of the domain in complex multiply-connected geometries remains problematic. In this research, three methods for evaluating the domain integrals associated with the boundary element analysis of the three-dimensional Poisson and nonhomogeneous Helmholtz equations in complex multiply-connected geometries are compared. The methods include the DRM, classical cell-based domain integration, and a novel auxiliary domain method. The auxiliary domain method allows the evaluation of the domain integral by constructing an approximately C
1 extension of the domain integrand into the complement of the multiply-connected domain. This approach combines the robustness and accuracy of direct domain integral evaluation while, at the same time, allowing for a relatively simple interior discretization. Comparisons are made between these three methods of domain integral evaluation in terms of speed and accuracy.
23 citations
TL;DR: The essence of the interactive particle enrichment algorithm is a particle insertion–deletion scheme that produces a visibility criterion for the description of a traction-free crack and leads to a better presentation of the ductile fracture process.
Abstract: This paper presents a combined continuous---discontinuous modeling technique for the dynamic ductile fracture analysis using an interactive particle enrichment algorithm and a strain-morphed nonlocal meshfree method The strain-morphed nonlocal meshfree method is a nodel-integrated meshfree method which was recently proposed for the analysis of elastic-damage induced strain localization problems In this paper, the strain-morphed nonlocal meshfree formulation is extended to the elastic---plastic-damage materials for the ductile fracture analysis When the ductile material is fully degraded, the interactive particle enrichment scheme is introduced in the strain-morphed nonlocal meshfree formulation that permits a continuous-to-discontinuous failure modeling The essence of the interactive particle enrichment algorithm is a particle insertion---deletion scheme that produces a visibility criterion for the description of a traction-free crack and leads to a better presentation of the ductile fracture process Several numerical benchmarks are examined using the explicit dynamics analysis to demonstrate the effectiveness and accuracy of the proposed method
23 citations