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 article, a boundary-type meshless method that combines the method of fundamental solutions and the dual reciprocity method with the RBFs has been developed, which provides a similar optimal accuracy in solving both 2D Poisson's and parabolic equations.
Abstract: The recent advance in the development of various kinds of meshless methods for solving partial differential equations has drawn attention of many researchers in science and engineering. One of the domain-type meshless methods is obtained by simply applying the radial basis functions (RBFs) as a direct collocation, which has shown to be effective in solving complicated physical problems with irregular domains. More recently, a boundary-type meshless method that combines the method of fundamental solutions and the dual reciprocity method with the RBFs has been developed. In this paper, the performances of these two meshless methods are compared and evaluated. Numerical results indicate that these two methods provide a similar optimal accuracy in solving both 2D Poisson's and parabolic equations.
99 citations
TL;DR: Computational methods for fluid-structure analysis are surveyed, and emphasis is placed on semi-discretization methods, such as finite element and finite difference methods.
98 citations
TL;DR: A penalty method which allows us to remove the free and moving boundary by adding a small and continuous penalty term to the Black‐Scholes equation is considered.
Abstract: We study the applicability of meshfree approximation schemes for the solution of multi‐asset American option problems. In particular, we consider a penalty method which allows us to remove the free and moving boundary by adding a small and continuous penalty term to the Black‐Scholes equation. Time discretization is achieved by a linearly implicit θ method. A comparison with results obtained recently by two of the authors using a linearly implicit finite difference method is included.
97 citations
TL;DR: In this article, a mesh-free Lagrangian method called smooth particle hydrodynamics (SPH) is used in numerical simulation to simulate the fragmentation of concrete due to explosive loading.
97 citations
TL;DR: The proper orthogonal decomposition variational multiscale element free Galerkin (POD-VMEFG) method for solving time-dependent incompressible Navier–Stokes equation is proposed and several test problems are given that show the acceptable accuracy and efficiency of the proposed scheme.
93 citations