Development of Gradient Smoothing Operations and Application to Biological Systems

Abstract

This thesis focuses on the development of gradient smoothing operations in weak and strong form and the application of these methods to model biological systems. The traditional finite element method (FEM) has some limitations such as ?overly-stiff? phenomenon and rigid reliance on elements. Through the gradient smoothing operations in the Galerkin weak form, the stiffness of FEM model can be reduced. Inspired by the attractive features of gradient smoothing operations in the Galerkin weak form, the gradient smoothing operations in strong form governing equations for fluid problems are proposed: piecewise linear gradient smoothing method (PL-GSM) and alpha gradient smoothing method (aGSM). Finally, a novel immersed gradient smoothing method (IGSM) that combines the gradient smoothing operation in weak and strong form is developed in this thesis to solve fluid structure interaction problems. All the numerical results in the gradient smoothing operations of weak and strong form are remarkably stable, accurate and robust.