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 More >

Peter W. Chung¹, Raju R. Namburu², Brian J. Henz³

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.1, pp. 45-62, 2004, DOI:10.3970/cmes.2004.005.045

Abstract A method is developed based on an additive modification to the first Lagrangian elasticity tensor to make the finite element method for hyperelasticity viable at the atomic length scale in the context of lattice statics. Through the definition of an overlap region, the close-ranged atomic interaction energies are consistently summed over the boundary of each finite element. These energies are subsequently used to additively modify the conventional material property tensor that comes from the second derivative of the stored energy function. The summation over element boundaries, as opposed to atom clusters, allows the mesh and More >

Yu.A. Melnikov, M.Yu. Melnikov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 291-306, 2001, DOI:10.3970/cmes.2001.002.291

Abstract The use of potential (integral) representations is studied when computing Green's functions for boundary value problems stated for Laplace and biharmonic equations over regions of complex configuration in two dimensions. The emphasis is on the non-traditional potentials, whose observation and source points occupy different sets. Such potentials reduce the original boundary value problems to functional (integral) equations with smooth kernels. Special integral representations are studied, the ones whose kernels are built not of the fundamental solutions of governing differential equations but of the Green's functions for simply shaped regions, which are associated with boundary value More >