Comparison between FEM and BEM for Real-time Simulation

Abstract

Computer simulation of object deformation has wide applications in areas such as movies, computer graphics, computer games, etc. Numerous methods have been proposed to simulate deformable objects. A common practice of simulating deformable objects is to use physically-based approaches which include the mass-spring system and the finite element method (FEM). The massspring system only gives a coarse estimation of object deformation whereas the FEM requires generating solid volumetric elements which is a tedious and time consuming process. The use of boundary element method (BEM) allows objects to be deformed without generating solid volumetric elements.In order to achieve real-time deformation, all these methods require time-consuming precomputation process. In this paper, a comparison is made between the FEM and the BEM techniques. We propose to adopt linear elements of boundary element technique for real-time applications. The method not only allows physically-based and real-time deformation, it also requires much shorter time for the pre-computation process. Experimental results show that the time required for the pre-computation process and real-time deformation can be enhanced significantly by adopting linear elements of BEM.

Simulating deformation of objects with multi‐materials using boundary element method

“…Thus, the time complexities for evaluating A −1 and D −1 are, respectively, O( p 3 ) and O(q 3 ). Therefore, when p q, the use of Equation (34) to compute A −1 greatly reduces the computing time [27].…”

“…where K fe is the combination of F f , F e , E f and E e , and K ku is the combinations of F u , F k , E u and E k . (27) and selecting the sub-matrices in matrix Vaccording to the indices of the common faces and edges that belong to the ith component, we have…”