Bilkent University
Department of Computer Engineering


Three-Dimensional Tetrahedral Mesh Deformation for Surgery Simulation Using Non-Linear Finite Element Method


Emir Gülümser
MSc Student Student
Computer Engineering Department
Bilkent University

Finite Element Method is a widely used numerical technique for finding approximate solutions to the complex problems of engineering and mathematical physics that cannot be solved with analytical methods. In most of the applications that requires simulation to be fast, linear FEM is preferred. Linear FEM works highly accurate with small deformations. However, linear FEM fails in accuracy when the large deformations are used. In this thesis, we presented both linear FEM and non-linear FEM in order to examine non-linear FEM's advantage over the linear FEM with using both small and large deformations. In order to make better analysis, linear FEM and non-linear FEM are both implemented with using tetrahedral elements. In addition, we do not use material nonlinearity with non-linear FEM. To state the effect of using the same material with nonlinear geometric properties, we only use geometric nonlinearity (Green-Lagrange strain definitions). In our experiments, it is shown that non-linear FEM gives more accurate results when compared to linear FEM. Moreover, the proposed non-linear solution achieved significant speed-ups for the calculation of stiffness matrices and for the solution of the whole system, compared to a state-of-the-art method. In terms of high accuracy, nonlinear FEM is the suitable method for crucial applications like surgical simulators.


DATE: 23 December, 2011, Friday @ 10:00