Journal ArticleDOI
Parallel meshfree computation for parabolic equations on graphics hardware
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TLDR
A parallel algorithm of the meshfree method for solving parabolic equations is developed that is the modified version of the radial point interpolation method, and the matrix assembly process in the algorithm is divided into smaller subprocesses that can be computed independently in parallel.Abstract:
The objective of this study is to develop a parallel algorithm of the meshfree method for solving parabolic equations. We assume that parallel computation is performed using graphics hardware, and the algorithm's design depends on the architecture of the device. The meshfree method employed in this study is the modified version of the radial point interpolation method, and the matrix assembly process in the algorithm is divided into smaller subprocesses that can be computed independently in parallel.read more
Citations
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Journal ArticleDOI
A finite-time convergent dynamic system for solving online simultaneous linear equations
TL;DR: The proposed dynamic system can achieve superior convergence performance and is called the finite-time convergent dynamic system, and the upper bound of the convergence time is derived analytically with the error bound being zero theoretically.
Journal ArticleDOI
Design and analysis of new complex zeroing neural network for a set of dynamic complex linear equations
TL;DR: A nonlinear sign-bi-power activation function is explored to enable the proposed NCZNN model to converge within finite time in complex domain by using two different ways, and simulative results verify the feasibility of the method in robotic applications.
Journal ArticleDOI
Solving time-varying nonlinear inequalities using continuous and discrete-time Zhang dynamics
Lin Xiao,Yunong Zhang +1 more
TL;DR: Numerical simulative examples demonstrate and verify the efficacy of the ZD models for solving time-varying and static scalar-valued nonlinear inequalities and the DTZD model possesses the lower complexity and higher accuracy, as compared with the Newton-type algorithm.
Journal ArticleDOI
An Improved Finite Time Convergence Recurrent Neural Network with Application to Time-Varying Linear Complex Matrix Equation Solution
TL;DR: In this paper, an improved finite time convergence zeroing neural network (FTCZNN) for online solving time-varying linear complex matrix equation (TVLCME) is realized.
References
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Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: In this article, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.
Journal ArticleDOI
A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics
Satya N. Atluri,T. Zhu +1 more
TL;DR: In this article, a local symmetric weak form (LSWF) for linear potential problems is developed, and a truly meshless method, based on the LSWF and the moving least squares approximation, is presented for solving potential problems with high accuracy.
Journal ArticleDOI
Generalizing the finite element method: Diffuse approximation and diffuse elements
TL;DR: The diffuse element method (DEM) as discussed by the authors is a generalization of the finite element approximation (FEM) method, which is used for generating smooth approximations of functions known at given sets of points and for accurately estimating their derivatives.
Book
Mesh Free Methods: Moving Beyond the Finite Element Method
TL;DR: In this paper, Galerkin et al. defined mesh-free methods for shape function construction, including the use of mesh-less local Petrov-Galerkin methods.
GPU Computing
TL;DR: The background, hardware, and programming model for GPU computing is described, the state of the art in tools and techniques are summarized, and four GPU computing successes in game physics and computational biophysics that deliver order-of-magnitude performance gains over optimized CPU applications are presented.