A new finite element level set method is developed to simulate the interface motion.The normal velocity of the moving interface can depend on both the local geometry,such as the curvature,and the external force such a...A new finite element level set method is developed to simulate the interface motion.The normal velocity of the moving interface can depend on both the local geometry,such as the curvature,and the external force such as that due to the flux from both sides of the interface of a material whose concentration is governed by a diffusion equation.The key idea of the method is to use an interface-fitted finite element mesh.Such an approximation of the interface allows an accurate calculation of the solution to the diffusion equation.The interface-fitted mesh is constructed from a base mesh,a uniform finite element mesh,at each time step to explicitly locate the interface and separate regions defined by the interface.Several new level set techniques are developed in the framework of finite element methods.These include a simple finite element method for approximating the curvature,a new method for the extension of normal velocity,and a finite element least-squares method for the reinitialization of level set functions.Application of the method to the classical solidification problem captures the dendrites.The method is also applied to the molecular solvation to determine optimal solute-solvent interfaces of solvation systems.展开更多
基金supported by the US National Science Foundation(NSF)through the grant DMS-0451466 and DMS-0811259by the US Department of Energy through the grant DE-FG02-05ER25707+2 种基金supported by the NSF Center for Theoretical Biological Physics(CTBP)under the NSF grant PHY-0822283the grant Award Number R01GM096188 from the National Institute of General Medical Sciences(NIGMS)the National Institutes of Health(NIH).
文摘A new finite element level set method is developed to simulate the interface motion.The normal velocity of the moving interface can depend on both the local geometry,such as the curvature,and the external force such as that due to the flux from both sides of the interface of a material whose concentration is governed by a diffusion equation.The key idea of the method is to use an interface-fitted finite element mesh.Such an approximation of the interface allows an accurate calculation of the solution to the diffusion equation.The interface-fitted mesh is constructed from a base mesh,a uniform finite element mesh,at each time step to explicitly locate the interface and separate regions defined by the interface.Several new level set techniques are developed in the framework of finite element methods.These include a simple finite element method for approximating the curvature,a new method for the extension of normal velocity,and a finite element least-squares method for the reinitialization of level set functions.Application of the method to the classical solidification problem captures the dendrites.The method is also applied to the molecular solvation to determine optimal solute-solvent interfaces of solvation systems.
