ABSTRACT
The finite element method (FEM) has very broad applications in a lot of research areas, and isogeometric analysis (IGA) is a new advancement based on FEM to integrate design with analysis. This chapter reviews the basic algorithm of finite element analysis (FEA) and its new developments, including IGA, extended FEM and immersed FEM. As a popular and powerful numerical method to solve partial differential equations over complex domains, FEM has been developed rapidly and used in many research areas including computational medicine, biology and engineering. The FEM is a general technique to solve boundary value problems with uniformly and non-uniformly spaced grids or meshes. In the implementation, the element stiffness matrix and element load vector are computed element by element, and then assembled together into the global stiffness matrix and global load vector. FEA has been applied broadly to study many biological and physical phenomena of biomolecular complexes such as simulating electrostatic potential distributions, and calcium signaling.
