首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >A new meshless 'fragile points method' and a local variational iteration method for general transient heat conduction in anisotropic nonhomogeneous media. Part I: Theory and implementation
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A new meshless 'fragile points method' and a local variational iteration method for general transient heat conduction in anisotropic nonhomogeneous media. Part I: Theory and implementation

机译:一种新的无丝石“脆弱点法”与各向异性非均匀介质一般瞬态导热的局部分析迭代方法。 第一部分:理论与实施

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摘要

A new and effective computational approach is presented for analyzing transient heat conduction problems. The approach consists of a meshless Fragile Points Method (FPM) being utilized for spatial discretization, and a Local Variational Iteration (LVI) scheme for time discretization. Anisotropy and nonhomogeneity do not give rise to any difficulties in the present implementation. The meshless FPM is based on a Galerkin weak-form formulation and thus leads to symmetric matrices. Local, very simple, polynomial and discontinuous trial and test functions are employed. In the meshless FPM, Interior Penalty Numerical Fluxes are introduced to ensure the consistency of the method. The LVIM in the time domain is a combination of the Variational Iteration Method (VIM) and a collocation method in each finitely large time interval. The present methodology represents a considerable improvement to the current state of science in computational transient heat conduction in anisotropic nonhomogeneous media. In this first part of the two-paper series, we focus on the theoretical formulation and implementation of the proposed methodology. Numerical results and validation are then presented in Part II.
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