{"title":"Linear Elasticity Problems Solved by Using the Fictitious Domain Method and Total - FETI Domain Decomposition","authors":"Lukas Mocek, Alexandros Markopoulos","volume":64,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":436,"pagesEnd":441,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/4891","abstract":"<p>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.<\/p>\r\n","references":"[1] Dostal Z.: Optimal quadratic programming algorithms: with applications\r\nto variational inequalities, Springer: New Your, 2009.\r\n[2] Dostal, Z.; Horak, D.; Kucera, R.; Total FETI - an easier implementable\r\nvariant of the FETI method for numerical solution of elliptic PDE,\r\nCommunications in Numerical Methods in Engineering, 22(12), 2006,\r\n1155-1162.\r\n[3] Farhat, C; Roux, FX; A method of finite element tearing and interconnecting\r\nand its parallel solution algorithm, International Journal for\r\nNumerical Methods in Engineering 1991; 32:12051227.\r\n[4] Glowinski, R.; Pan, Tsorn-Whay; Periaux, J.; A fictitious domain method\r\nfor Dirichlet problem and applications, Computing, Volume 84, Numbers\r\n1-2, 2008, 69-96.\r\n[5] Haslinger, J.; Mkinen, R. A. E.; Introduction to shape optimization:\r\ntheory, approximation, and computation, SIAM, 2003\r\n[6] Haslinger, J.; Kozubek, T.; Kucera, R.; Peichl, G.; Projected the Schur\r\ncomplement method for solving non-symmetric systems arising from a\r\nsmooth fictitious domain approach.. Lin. Algebra Appl., 14(2007), 713-\r\n739.\r\n[7] Kozubek, T.; Vondrak, V.; Mensik, M.; Horak, D.; Dostal, Z.; Hapla, V.;\r\nKabelikova, P.; Cermak, M.; Total FETI domain decomposition method\r\nand its massively parallel implementation, Computers and Structures,\r\nsubmitted\r\n[8] Kozubek T, Markopoulos A, Brzobohaty T, Kucera R, Vondrak V, Dostal\r\nZ. MatSol - MATLAB effcient solvers for problems in engineering.\r\nhttp:\/\/matsol.vsb.cz.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 64, 2012"}