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: In this paper, a fully automatic method of selecting the stencils from anisotropic point distributions, which are obtained from overlapping structured grids, is outlined The original connectivity and the concept of a resolving direction are used to help construct good quality stencil with limited user input.
Abstract: Meshless methods are attractive for simulating moving body problems The selection of the stencils over the domain for the meshless solver is crucial for the method to be competitive with established computational fluid dynamics techniques Stencil selection is relatively straightforward if the point distributions are isotropic in nature, however, this is rarely the case in computations that solve the Navier–Stokes equations In this paper, a fully automatic method of selecting the stencils from anisotropic point distributions, which are obtained from overlapping structured grids, is outlined The original connectivity and the concept of a resolving direction are used to help construct good quality stencils with limited user input
15 citations
01 Jan 1999
TL;DR: In this paper, a mesh-less method for conservation laws was proposed, with the only requirement that the ratio of the smoothing length to the characteristic size of the mesh be bounded.
Abstract: This paper is devoted to analyse new meshless methods. They generalize classical weighted particle methods for conservation laws. We prove that they can be both conservative and consistent. We obtain convergence of the methods in scalar case with the only requirement that the ratio of the smoothing length (or size of the cut-off) to the characteristic size of the mesh be bounded. Applications for Euler equations are proposed.
15 citations
TL;DR: An element-free Galerkin method (EFGM) is proposed to simulate the propagation of myocardial electrical activation without explicit mesh constraints using a monodomain model.
Abstract: An element-free Galerkin method (EFGM) is proposed to simulate the propagation of myocardial electrical activation without explicit mesh constraints using a monodomain model. In our framework the geometry of myocardium is first defined by a meshfree particle representation that is, a sufficient number of sample nodes without explicit connectivities are placed in and inside the surface of myocardium. Fiber orientations and other material properties of myocardium are then attached to sample nodes according to their geometrical locations, and over the meshfree particle representation spatial variation of these properties is approximated using the shape function of EFGM. After the monodomain equations are converted to their Galerkin weak form and solved using EFGM, the propagation of myocardial activation can be simulated over the meshfree particle representation. The derivation of this solution technique is presented along a series of numerical experiments and a solution of monodomain model using a FitzHugh-Nagumo (FHN) membrane model in a canine ventricular model and a human-heart model which is constructed from digitized virtual Chinese dataset.
15 citations
TL;DR: In this paper, the authors focus on numerical analysis of dynamic fracture of thin-walled structures such as pipes and pressure vessels and propose a mesh-free method that has advantages because its higher order continuity and smoothness and its opportunities to model fracture in a simple way.
Abstract: Analysis and reliability assessment of fracturing thin-walled structures is important in engineering science. We focus on numerical analysis of dynamic fracture of thin-walled structures such as pipes and pressure vessels. Instead of using finite element method, we propose meshfree method that has advantages because its higher order continuity and smoothness and its opportunities to model fracture in a simple way. Therefore, connectivity between adjacent nodes are simply removed once fracture criterion is met. The main advantage of our meshfree method is its simplicity and robustness.
15 citations
TL;DR: In this paper, numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition are discussed. But the results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results.
Abstract: Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank-Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193–202, 2002; DOI 10.1002/num.1040
15 citations