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作者:G. R. Liu
来源:[J].International Journal of Computational Methods(IF 0.481), 2016, Vol.13 (02)World Scientific Publishing
摘要:This paper discusses the Partitions of Unity (PU) property that is one of the most important properties of nodal shape functions used in various numerical methods via discretization, including element-based and/or meshfree methods, such as FEM, S-FEM, S-PIM, EFG, XFEM, etc. The s...
作者:G. R. Liu
来源:[J].International Journal of Computational Methods(IF 0.481), 2016, Vol.13 (05)World Scientific Publishing
摘要:This review paper presents a methodological study on possible and existing meshfree methods for solving the partial differential equations (PDEs) governing solid mechanics problems, based mainly on the research work in the past two decades at the authors group. We start with a di...
作者:G. R. Liu
来源:[J].International Journal of Computational Methods(IF 0.481), 2018, Vol.15 (03)World Scientific Publishing
摘要:In order to solve partial differential equations (PDEs) numerically, one first needs to approximate the field functions (such as the displacement functions), and then obtain the derivatives of the field functions (such as the strains), by directly differentiating the field f...
作者:G. R. Liu
来源:[J].International Journal of Computational Methods(IF 0.481), 2019, Vol.16 (08), pp.21World Scientific Publishing
摘要:Recent breakthroughs in deep-learning algorithms enable dreams of artificial intelligence (AI) getting close to reality. AI-based technologies are now being developed rapidly, including service and industrial robots, autonomous and self-driving vehicles. This work proposes Two-Wa...
作者:Meng Chen , Ming Li , G. R. Liu
来源:[J].International Journal of Computational Methods(IF 0.481), 2016, Vol.13 (04)World Scientific Publishing
摘要:This paper represents some basic mathematic theories for G s spaces of functions that can be used for weakened weak (W2) formulations, upon which the smoothed finite element methods (S-FEMs) and the smoothed point interpolation methods (S-PIMs) are based for solvi...
作者:R. P. Niu , G. R. Liu , M. Li
来源:[J].International Journal of Computational Methods(IF 0.481), 2016, Vol.13 (02)World Scientific Publishing
摘要:The paper proposes a general formulation for simulating unsteady state heat transfer problem with moving boundaries. The method is equipped with a correction term based on the finite element method. In dealing with the unsteady behavior, forward time marching is performed using t...
作者:G. F. Sun , G. R. Liu , M. Li
来源:[J].International Journal of Computational Methods(IF 0.481), 2016, Vol.13 (02)World Scientific Publishing
摘要:In this paper, a novel explicit finite-difference (FD) method is presented to approximate the positive and bounded growth of biological films that is governed by partial differential equations (PDEs) with a nonlinear density-dependent diffusion reaction rate. In such a unique non...
作者:... Z. Q. Zheng , Y. T. Gu , G. R. Liu
来源:[J].International Journal of Computational Methods(IF 0.481), 2016, Vol.13 (05)World Scientific Publishing
摘要:It is well known that a high-order point interpolation method (PIM) based on the standard Galerkin formations is not conforming, and thus the solution may not always be convergent. This paper proposes a new interesting technique called quasi-conforming point interpolation method ...
作者:... Shiwei Zhou , G. R. Liu , Q. Li
来源:[J].International Journal of Computational Methods(IF 0.481), 2016, Vol.13 (02)World Scientific Publishing
摘要:Periodic microstructural composites have gained considerable attention in material science and engineering attributable to their excellent flexibility in tailoring various desirable physical properties. Conventionally, the finite element technique has been widely used in implemen...
作者:... Huiming Ning , Ning Hu , G. R. Liu
来源:[J].International Journal of Computational Methods(IF 0.481), 2017, Vol.14 (04)World Scientific Publishing
摘要:A three-dimensional (3D) Computational Fluid Dynamics (CFD) solver based on the gradient smoothing method (GSM) is developed for compressible flows based on previous research. The piecewise constant smoothing function with one-point integration scheme is implemented for gradient ...

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