Jun Lv

TL;DR: In this article, a new numerical method, Element Differential Method (EDM), is proposed for solving general heat conduction problems with variable conductivity and heat source subjected to various boundary conditions.

TL;DR: In this paper, a new numerical method, Element Differential Method (EDM), is proposed for solving general thermal-mechanical problems, which is the direct differentiation of the shape functions of Lagrange isoparametric elements used to characterize the geometry and physical variables.

TL;DR: A new numerical method, named as the Free Element Collocation Method (FECM), is proposed for solving general engineering problems governed by the second order partial differential equations (PDEs), which can result in more stable results than the traditional collocation method.

TL;DR: In this paper, the element differential method is extended to solve a transient nonlinear heat conduction problem with a heat source and temperature-dependent thermophysical properties for the first time, where the transient term is discretized by employing a finite difference scheme.

TL;DR: In this paper, an extended multiscale finite element method is developed to solve the mechanical behaviors of heterogeneous materials with randomly distributed polygonal microstructure, where a type of rational oversampling technique is imposed to calculate the oscillatory boundary conditions for the construction of multiscales base functions.