Zhuo-Jia Fu

Bio: Zhuo-Jia Fu is an academic researcher from Hohai University. The author has contributed to research in topics: Singular boundary method & Collocation method. The author has an hindex of 26, co-authored 95 publications receiving 2213 citations. Previous affiliations of Zhuo-Jia Fu include Nanjing University of Aeronautics and Astronautics & Chinese Academy of Sciences.

Recent Advances in Radial Basis Function Collocation Methods

Abstract: Radial basis functions (RBFs) are constructed in terms of one-dimensional distance variable and appear to have certain advantages over the traditional coordinates-based functions. In contrast to the traditional meshed-based methods, the RBF collocation methods are mathematically simple and truly meshless, which avoid troublesome mesh generation for high-dimensional problems involving irregular or moving boundary. This opening chapter begins with the introduction to RBF history and its applications in numerical solution of partial differential equations and then gives a general overview of the book.

A boundary-type meshless solver for transient heat conduction analysis of slender functionally graded materials with exponential variations

Abstract: This study presents a parallel meshless solver for transient heat conduction analysis of slender functionally graded materials (FGMs) with exponential variations. In the present parallel meshless solver, a strong-form boundary collocation method, the boundary knot method (BKM), in conjunction with Laplace transform is implemented to solve the heat conduction equations of slender FGMs with exponential variations. This method is mathematically simple, easy-to-parallel, meshless, and without domain discretization. However, two ill-posed issues, the ill-conditioning dense BKM matrix and numerical inverse Laplace transform process, may lead to incorrect numerical results. Here the extended precision arithmetic (EPA) and the domain decomposition method (DDM) have been adopted to alleviate the effect of these two ill-posed issues on numerical efficiency of the present method. Then the parallel algorithm has been employed to significantly reduce the computational cost and enhance the computational capacity for the FGM structures with larger length-width ratio. To demonstrate the effectiveness of the present parallel meshless solver for transient heat conduction analysis, several benchmark examples are considered under slender FGMs with exponential variations. The present results are compared with the analytical solutions, the conventional boundary knot method and COMSOL simulation.

Fast parallel algorithms for short-range molecular dynamics

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Solving PDEs with radial basis functions

Abstract: Finite differences provided the first numerical approach that permitted large-scale simulations in many applications areas, such as geophysical fluid dynamics. As accuracy and integration time requirements gradually increased, the focus shifted from finite differences to a variety of different spectral methods. During the last few years, radial basis functions, in particular in their ‘local’ RBF-FD form, have taken the major step from being mostly a curiosity approach for small-scale PDE ‘toy problems’ to becoming a major contender also for very large simulations on advanced distributed memory computer systems. Being entirely mesh-free, RBF-FD discretizations are also particularly easy to implement, even when local refinements are needed. This article gives some background to this development, and highlights some recent results.

Recent Advances in Radial Basis Function Collocation Methods

Abstract: Radial basis functions (RBFs) are constructed in terms of one-dimensional distance variable and appear to have certain advantages over the traditional coordinates-based functions. In contrast to the traditional meshed-based methods, the RBF collocation methods are mathematically simple and truly meshless, which avoid troublesome mesh generation for high-dimensional problems involving irregular or moving boundary. This opening chapter begins with the introduction to RBF history and its applications in numerical solution of partial differential equations and then gives a general overview of the book.