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 >

Cosmina S. Hogea¹, Bruce T. Murray¹, James A. Sethian^2,3

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.2, pp. 109-130, 2005, DOI:10.3970/fdmp.2005.001.109

Abstract A computational framework for simulating growth and transport in biological materials based on continuum models is proposed. The advantages of the finite difference methodology employed are generality and relative simplicity of implementation. The Cartesian mesh/level set method developed here provides a computational tool for the investigation of a host of transport-based tissue/tumor growth models, that are posed as free or moving boundary problems and may exhibit complicated boundary evolution including topological changes. The methodology is tested here on a widely studied "incompressible flow" type tumor growth model with a numerical implementation in two dimensions; comparisons with results obtained from a… More >