Michael Yu Wang¹, Xiaoming Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.4, pp. 373-396, 2004, DOI:10.3970/cmes.2004.006.373

Abstract This paper addresses the problem of structural shape and topology optimization. A level set method is adopted as an alternative approach to the popular homogenization based methods. The paper focuses on four areas of discussion: (1) The level-set model of the structure’s shape is characterized as a region and global representation; the shape boundary is embedded in a higher-dimensional scalar function as its “iso-surface.” Changes of the shape and topology are governed by a partial differential equation (PDE). (2) The velocity vector of the Hamilton-Jacobi PDE is shown to be naturally related to the shape derivative from the classical shape… More >

V. Kozulić¹, H. Gotovac¹, B. Gotovac¹

CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 51-70, 2007, DOI:10.3970/cmc.2007.006.051

Abstract In this paper, we present a multi-resolution adaptive algorithm for solving problems described by partial differential equations. The technique is based on the collocation method using Fup basis functions, which belong to a class of Rvachev's infinitely differentiable finite functions. As it is possible to calculate derivation values of Fup basis functions of high degree in a precise yet simple way, so it is possible to efficiently apply strong formulation procedures. The mesh free method developed in this work is named Adaptive Fup Collocation Method (AFCM). The distribution of collocation points within the observed area is changed adaptively, depending on… More >