Linear Elasticity Problems Solved by Using the Fictitious Domain Method and Total - FETI Domain Decomposition

The main goal of this paper is to show a possibility, how to solve numerically elliptic boundary value problems arising in 2D linear elasticity by using the fictitious domain method (FDM) and the Total-FETI domain decomposition method. We briefly mention the theoretical background of these methods and demonstrate their performance on a benchmark.

• Lukas Mocek
• Alexandros Markopoulos

• Linear elasticity
• fictitious domain method
• Total-FETI
• domain decomposition
• saddle-point system.

[1] Dostal Z.: Optimal quadratic programming algorithms: with applications
to variational inequalities, Springer: New Your, 2009.
[2] Dostal, Z.; Horak, D.; Kucera, R.; Total FETI - an easier implementable
variant of the FETI method for numerical solution of elliptic PDE,
Communications in Numerical Methods in Engineering, 22(12), 2006,
1155-1162.
[3] Farhat, C; Roux, FX; A method of finite element tearing and interconnecting
and its parallel solution algorithm, International Journal for
Numerical Methods in Engineering 1991; 32:12051227.
[4] Glowinski, R.; Pan, Tsorn-Whay; Periaux, J.; A fictitious domain method
for Dirichlet problem and applications, Computing, Volume 84, Numbers
1-2, 2008, 69-96.
[5] Haslinger, J.; Mkinen, R. A. E.; Introduction to shape optimization:
theory, approximation, and computation, SIAM, 2003
[6] Haslinger, J.; Kozubek, T.; Kucera, R.; Peichl, G.; Projected the Schur
complement method for solving non-symmetric systems arising from a
smooth fictitious domain approach.. Lin. Algebra Appl., 14(2007), 713-
739.
[7] Kozubek, T.; Vondrak, V.; Mensik, M.; Horak, D.; Dostal, Z.; Hapla, V.;
Kabelikova, P.; Cermak, M.; Total FETI domain decomposition method
and its massively parallel implementation, Computers and Structures,
submitted
[8] Kozubek T, Markopoulos A, Brzobohaty T, Kucera R, Vondrak V, Dostal
Z. MatSol - MATLAB effcient solvers for problems in engineering.
http://matsol.vsb.cz.