Some Use Cases for Composite Finite Elements in Image Based Computing
Many bio-medical simulations involve structures of complicated shape. Frequently, the geometry information is given by radiological images. A particular challenge for model discretization in this context is generating appropriate computational meshes.One efficient approach for Finite Element simulations avoiding meshing is the Composite Finite Element approach that has been developed and implemented for image based simulations during the past decade. In the present paper, we provide an overview of previous own work in this field, summarizing the method and showing selected applications: simulation of radio-frequency ablation including vaporization, simulation of elastic deformation of trabecular bone, and numerical homogenization of material properties for the latter.
KeywordsTrabecular Bone Representative Volume Element Finite Element Space Discontinuous Coefficient Multigrid Solver
We acknowledge Martin Rumpf, Stefan Sauter, and Uwe Wolfram for their collaboration and many fruitful and inspiring discussions regarding CFE and their applications.
- 1.G. Allaire, Shape Optimization by the Homogenization Method. Applied Mathematical Sciences, vol. 146 (Springer, New York, 2002)Google Scholar
- 15.T. Kröger, I. Altrogge, T. Preusser, P.L. Pereira, D. Schmidt, A. Weihusen, H.O. Peitgen, Numerical simulation of radio frequency ablation with state dependent material parameters in three space dimensions, in MICCAI (2), ed. by R. Larsen, M. Nielsen, J. Sporring. Lecture Notes in Computer Science, vol. 4191 (Springer, New York, 2006), pp. 380–388Google Scholar
- 17.X. Li, J. Lowengrub, A. Rätz, A. Voigt, Solving PDEs in complex geometries: a diffuse domain approach. Commun. Math. Sci. 7(1), 81 (2009)Google Scholar
- 21.T. Preusser, M. Rumpf, L.O. Schwen, Finite element simulation of bone microstructures, in Proceedings of the 14th Workshop on the Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields, University of Ulm, July 2007, pp. 52–66Google Scholar
- 22.A.G. Rumpf, Institute for Numerical Simulation, University of Bonn: Quocmesh software library. http://numod.ins.uni-bonn.de/software/quocmesh/index.html
- 23.M. Rumpf, L.O. Schwen, H.J. Wilke, U. Wolfram, Numerical homogenization of trabecular bone specimens using composite finite elements, in The International Journal of Multiphysics, Special Edition: Multiphysics Simulations – Advanced Methods for Industrial Engineering. Selected Contributions from 1st Fraunhofer Multiphysics Conference, 2010, pp. 127–143Google Scholar
- 26.L.O. Schwen, Composite finite elements for trabecular bone microstructures. Ph.D. thesis, University of Bonn, 2010Google Scholar
- 27.L.O. Schwen, T. Pätz, T. Preusser, Composite finite element simulation of radio frequency ablation and bone elasticity, in Proceedings of the 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna, ed. by J. Eberhardsteiner, et al., September 2012Google Scholar
- 28.L.O. Schwen, T. Preusser, M. Rumpf, Composite finite elements for 3D elasticity with discontinuous coefficients, in Proceedings of the 16th Workshop on the Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields, University of Ulm, 2009Google Scholar
- 30.L.O. Schwen, U. Wolfram, H.J. Wilke, M. Rumpf, Determining effective elasticity parameters of microstructured materials, in Proceedings of the 15th Workshop on the Finite Element Method in Biomedical Engineering, Biomechanics and Related Fields, University of Ulm, July 2008, pp. 41–62Google Scholar
- 32.T.Stein, Untersuchungen zur Dosimetrie der hochfrequenzstrominduzierten interstitiellen Thermotherapie in bipolarer Technik. Ecomed (2000)Google Scholar