Comparison of FEM and BEM for interactive object simulation
There are two major approaches for real-time object simulation namely, the geometry (non-physically) based and the physically based approaches. Geometry based approaches such as free-form deformation (FFD) employ purely geometric techniques to model deformation. Physically based approaches usually adopt massspring system, finite element method (FEM) or boundary element method (BEM) for simulation. The massspring system is simple and only gives a coarse estimation of object deformation. Recently, FEM and BEM have been extensively used in object simulation because of the demand for more realistic simulation. However, a major drawback of FEM and BEM is their difficulty to achieve real-time deformation. In this article, we compare two different physically based approaches, FEM and BEM, according to their accuracy and computational complexity. Several experiments were conducted to compare the time required for the pre-computation process and the deformation process. In addition, the BEM with linear boundary elements is implemented and tested. At the current state of investigation, for the meshes with triangular elements, BEM with linear boundary elements is significantly faster than BEM with constant boundary elements under most of the circumstances. With the band matrix of FEM, the pre-computation process is faster than the BEM for a model with small mesh size. However if the mesh size of the model is large, the pre-computation process of BEM with linear boundary elements is the fastest.
physically based boundary element method computational complexity linear boundary elements constant boundary elements stiffness matrix