To solve numerically boundary value problems requires discretizing the solution domain into elements through which low order approximation is valid. This is the basic idea of the finite element method (FEM). However, discretizing can become
expensive when the boundary moves, or repeated meshing is necessary. The finite cell method is a high order version of FEM specifically designed and tuned for extended domains which can be discretized routinely with relatively low cost. Problems that may arise stem in the mechanisms of imposing boundary conditions, or in integration procedures that are defined for homogeneous domains. Techniques have been developed and reported to overcome these difficulties. The performance of the method however� is similar to the high order FEM while the convergence is fast and at least for regular cases, exponential. Figure 1 shows a perforated domain enveloped by a rectangular domain which is discretized by four cells. The error in the energy norm diminished exponentially
by increasing the order of the approximation polynomials.
Research Partners:
Prof. Dr. Jamshid Parvizian, Isfahan University of Technology
Prof. Dr.-Ing. habil. Alexander Duester, Technische Universit�t Hamburg
Prof. Dr. rer.nat. Ernst Rank, Technische Universit�t Muenchen
Prof. Dr. Hasan Nahvi, Isfahan University of Technology
Prof. Dr. Mohammad Mashayekhi, Isfahan University of Technology
Mr. A. Abedian, Phd candidate, Isfahan University of Technology
Mrs M. Ranjbar, Phd candidate, Isfahan University of Technology
Mr. Y. Mirbagheri, Phd candidate, Isfahan University of Technology
Publications on FCM:
� J. Parvizian, A. Duester, E. Rank. Topology Optimization Using Finite Cell Method, Engineering and Optimization,� 2011.
� A. Duester, A. Abedian, J. Parvizian, E. Rank. On adaptive integration schemes for the Finite Cell Method, TCCM2011, 12-14 Sep. 2011, Padua, Italy.
� A. Abedian, J. Parvizian, A. Duester, E. Rank. Adaptive integration and application to problems of elastoplasticity, HOFEIM 2011, Cracow, Poland.
� A. Abedian, J. Parvizian, A. Duester, H. Khademyzadeh, E. Rank. Finite Cell Method for Elasto-Plastic Problems. Proceedings of the Tenth International Conference on Computational Structures Technology, Valencia, Spain, September 14-17, 2010.
� A. Duester, J. Parvizian, E. Rank. Topology optimization based on the finite cell method. Proceedings in Applied Mathematics and Mechanics, 10:151-152, 2010.
� A. Duester, J. Parvizian, Z. Yang, E. Rank. The Finite Cell Method for 3D problems of solid mechanics. Computer Methods in Applied Mechanics and Engineering, 197:3768-3782, 2008.��
� A. Duester, J. Parvizian, Z. Yang, E. Rank. A high order fictitious domain method for patient specific surgery planning. Proceedings of APCOM'07 in conjunction with EPMESC XI, Japan, December 3-6, 2007.
� J. Parvizian, A. Duester, E. Rank. Finite Cell Method: h- and p-extension for embedded domain problems in Solid��� Mechanics. Computational Mechanics, 41: 121-133, 2007.
� Parvizian J., Duester A. & Rank E. The finite cell method for singular cases in solid mechanics. ECCOMAS Thematic Conference on Meshless Methods, Porto, Portugal, 9-11 July, 2007.
� Rank E., Parvizian J., Yang Z. & Duester A. A High Order Embedded Domain Method. International Workshop on High-Order Finite Element Methods, Herrsching, Munich, 17-19 May, 2007.
� Duester A., Parvizian J., Rank E. & Yang Z. The Finite Cell Method for Orthopedic Simulation. Mini-symposium on Higher Order and hp Methods with Applications to Elliptic� and Maxwell Problems, 9th US National Congress on Computational Mechanics, San Francisco, CA, July 23-26, 2007.
� Parvizian J., Duester A. & Rank E. Finite Cell Method for Smooth and Singular Problems. The 12th conference on the Mathematics of Finite Elements and
This research is supported by Alexander von Humboldt Foundation through an institutional partnership program.