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D. Horak^1,2, Z. Dostal^1,2, V. Hapla¹, J. Kruzik¹, R. Sojka¹ and M. Cermak¹

¹IT4Innovations, VSB-Technical University of Ostrava, Czech Republic
²Department of Applied Mathematics, VSB-Technical University of Ostrava, Czech Republic

doi:10.4203/ccp.111.8

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D. Horak, Z. Dostal, V. Hapla, J. Kruzik, R. Sojka, M. Cermak, "Projector-less TFETI for Contact Problems: Preliminary Results", in , (Editors), "Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 8, 2017. doi:10.4203/ccp.111.8

Keywords: Projector-less TFETI, TFETI, contact problems, Moore-Penrose pseudoinverse, orthogonal projectors, PERMON.

Summary

The FETI methods turned out to be very efficient for the solution of large problems arising from the discretization of elliptic partial differential equations (PDEs), but their parallel scalability can be degraded by the increasing cost of the projectors containing coarse problem (CP) solution. If applied to discretized variational inequalities, the relevant quadratic programming (QP) problems employing FETI methods can be solved by means of the MPRGP and SMALBE algorithms. The Hessian matrix contains three projector applications that can be implemented using two CP solutions. These QP algorithms and FETI methods are implemented in our PERMON software package based on PETSc. The paper deals with the modification of the TFETI method that eliminates applications of the projectors while the numerical scalability of the solver is preserved. This can be achieved by using the Moore-Penrose pseudoinverse, obtainable by projecting the input vector onto the range of the stiffness matrix. This operation is purely local and very cheap. Numerical experiments demonstrating performance of this new approach are presented.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 111 PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING Edited by: Paper 8 Projector-less TFETI for Contact Problems: Preliminary Results D. Horak^1,2, Z. Dostal^1,2, V. Hapla¹, J. Kruzik¹, R. Sojka¹ and M. Cermak¹ ¹IT4Innovations, VSB-Technical University of Ostrava, Czech Republic ²Department of Applied Mathematics, VSB-Technical University of Ostrava, Czech Republic doi:10.4203/ccp.111.8 purchase the full-text of this paper Full Bibliographic Reference for this paper D. Horak, Z. Dostal, V. Hapla, J. Kruzik, R. Sojka, M. Cermak, "Projector-less TFETI for Contact Problems: Preliminary Results", in , (Editors), "Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 8, 2017. doi:10.4203/ccp.111.8 Keywords: Projector-less TFETI, TFETI, contact problems, Moore-Penrose pseudoinverse, orthogonal projectors, PERMON. Summary The FETI methods turned out to be very efficient for the solution of large problems arising from the discretization of elliptic partial differential equations (PDEs), but their parallel scalability can be degraded by the increasing cost of the projectors containing coarse problem (CP) solution. If applied to discretized variational inequalities, the relevant quadratic programming (QP) problems employing FETI methods can be solved by means of the MPRGP and SMALBE algorithms. The Hessian matrix contains three projector applications that can be implemented using two CP solutions. These QP algorithms and FETI methods are implemented in our PERMON software package based on PETSc. The paper deals with the modification of the TFETI method that eliminates applications of the projectors while the numerical scalability of the solver is preserved. This can be achieved by using the Moore-Penrose pseudoinverse, obtainable by projecting the input vector onto the range of the stiffness matrix. This operation is purely local and very cheap. Numerical experiments demonstrating performance of this new approach are presented. purchase the full-text of this paper (price £22) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £45 +P&P)
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