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, accurate and efficient algorithms based on global and local meshless formulations with modified Levin's quadrature are proposed for numerical solution of two-dimensional highly oscillatory Fredholm integral equations.
Abstract: In this paper, accurate and efficient algorithms based on global and local meshless formulations with modified Levin׳s quadrature are proposed for numerical solution of two-dimensional highly oscillatory Fredholm integral equations. The main focus of the study is to extend applications of global and local meshless procedures to integral equations on uniform as well as irregular nodes. This work will also focus on undertaking a comparative performance of the global and local meshless methods. The proposed methods will be tested on different test problems having phase function free of stationary points. From the numerical results we will draw some conclusions about accuracy and robustness of the proposed approaches. Further, the computational cost and the singularity of the system matrices in terms of condition number of both the local and global meshless methods will be investigated. A comprehensive analysis will ultimately establish computational efficiency and accuracy of the local approach.
20 citations
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TL;DR: The boundary knot method is a promising mesh-free, integration-free boundary-type technique for the solution of partial differential equations as mentioned in this paper, which looks for an approximation of the solution in the linear span of a set of specialized radial basis functions that satisfy the governing equation of the problem.
Abstract: The boundary knot method is a promising meshfree, integration-free, boundary-type technique for the solution of partial differential equations. It looks for an approximation of the solution in the linear span of a set of specialized radial basis functions that satisfy the governing equation of the problem. The boundary conditions are taken into account through the collocation technique. The specialized radial basis function for harmonic elastic and viscoelastic problems is derived, and a boundary knot method for the solution of these problems is proposed. The completeness issue regarding the proposed set of radial basis functions is discussed, and a formal proof of incompleteness for the circular ring problem is presented. In order to address the numerical performance of the proposed method, some numerical examples considering simple and complex domains are solved.
20 citations
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TL;DR: In this paper, the authors proposed a localized radial basis function (RBF) partition of unity method for partial integro-differential equation (PIDE) problems in jump-diffusion model.
20 citations
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TL;DR: A new reduced order model based on the meshless numerical procedure for solving an important model in fluid mechanics is developed and the reduction in CPU time as well as the efficiency of the proposed method is investigated to investigate two-dimensional cases.
20 citations
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31 Jan 2019
TL;DR: A local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs, which has flexibility with respect to geometry along with high order of convergence rate.
Abstract: In this paper, a local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs. This local approach has flexibility with respect to geometry along with high order of convergence rate. In case of global meshless methods, the two major deficiencies are the computational cost and the optimum value of shape parameter. Therefore, research is currently focused towards localized RBFs approximations, as proposed here. The proposed local meshless procedure is used for spatial discretization, whereas for temporal discretization, different time integrators are employed. The proposed local meshless method is testified in terms of efficiency, accuracy and ease of implementation on regular and irregular domains.
20 citations