A preconditioner for a FETI-DP method for mortar element discretization of a 4th order problem in 2D.

In this paper a parallel preconditioner for a FETI-DP formulation for a mortar discretization of a fourth order problem is presented and analyzed. We show that the condition number of the preconditioned FETI-DP operator is proportional to , where and are mesh sizes.

[1]  R. Tezaur Analysis Of Lagrange Multiplier Based Domain Decomposition , 1998 .

[2]  Faker Ben Belgacem,et al.  The Mortar finite element method with Lagrange multipliers , 1999, Numerische Mathematik.

[3]  Chang-Ock Lee,et al.  Preconditioners for the dual-primal FETI methods on nonmatching grids: Numerical study , 2006, Comput. Math. Appl..

[4]  Patrick Le Tallec,et al.  A Neumann--Neumann Domain Decomposition Algorithm for Solving Plate and Shell Problems , 1995 .

[5]  Barbara I. Wohlmuth,et al.  Discretization Methods and Iterative Solvers Based on Domain Decomposition , 2001, Lecture Notes in Computational Science and Engineering.

[6]  Charbel Farhat,et al.  A scalable dual-primal domain decomposition method , 2000, Numerical Linear Algebra with Applications.

[7]  Leszek Marcinkowski An additive Schwarz method for mortar Morley finite element discretizations of 4th order elliptic problem in 2D. , 2007 .

[8]  Jan Mandel,et al.  On the convergence of a dual-primal substructuring method , 2000, Numerische Mathematik.

[9]  Non-matching Grids and Lagrange Multipliers , 2005 .

[10]  Susanne C. Brenner,et al.  The condition number of the Schur complement in domain decomposition , 1999, Numerische Mathematik.

[11]  Andrea Toselli,et al.  Domain decomposition methods : algorithms and theory , 2005 .

[12]  L. R. Scott,et al.  The Mathematical Theory of Finite Element Methods , 1994 .

[13]  Chang-Ock Lee,et al.  A Preconditioner for the FETI-DP Formulation with Mortar Methods in Two Dimensions , 2004, SIAM J. Numer. Anal..

[14]  Wenbin Chen,et al.  A Multigrid Method for the Mortar-Type Morley Element Approximation of a Plate Bending Problem , 2001, SIAM J. Numer. Anal..

[15]  Maksymilian Dryja,et al.  A Neumann-Neumann algorithm for a mortar discretization of elliptic problems with discontinuous coefficients , 2005, Numerische Mathematik.

[16]  Olof B. Widlund,et al.  A generalized FETI-DP method for a mortar discretization of elliptic problems , 2003 .

[17]  Olof B. Widlund,et al.  Two-Level Schwarz Algorithms with Overlapping Subregions for Mortar Finite Elements , 2006, SIAM J. Numer. Anal..

[18]  Olof B. Widlund,et al.  Iterative Substructuring Preconditioners For Mortar Element Methods In Two Dimensions , 1997 .

[19]  Olof B. Widlund,et al.  DUAL-PRIMAL FETI METHODS FOR THREE-DIMENSIONAL ELLIPTIC PROBLEMS WITH HETEROGENEOUS COEFFICIENTS , 2022 .

[20]  Leszek Marcinkowski A Mortar Finite Element Method for Fourth Order Problems in Two Dimensions with Lagrange Multipliers , 2005, SIAM J. Numer. Anal..

[21]  Yvon Maday,et al.  The mortar element method for three dimensional finite elements , 1997 .

[22]  Jianguo Huang,et al.  On mortar-type Morley element method for plate bending problem , 2001 .

[23]  Zakaria Belhachmi Nonconforming Mortart Element Methods for the Spectral Discretization of Two-Dimensional Fourth-Order Problems , 1997 .

[24]  Wlodzimierz Proskurowski,et al.  On preconditioners for mortar discretization of elliptic problems , 2003, Numer. Linear Algebra Appl..

[25]  Nina N. Dokeva,et al.  A FETI-DP Method for Mortar Finite Element Discretization of a Fourth Order Problem , 2008 .

[26]  Axel Klawonn,et al.  The FETI methods for Mortar Finite Elements , 1999 .

[27]  Leszek Marcinkowski,et al.  A mortar element method for some discretizations of a plate problem , 2002, Numerische Mathematik.

[28]  Talal Rahman,et al.  Additive Schwarz Methods for Elliptic Mortar Finite Element Problems , 2003, Numerische Mathematik.

[29]  Leszek Marcinkowski Domain Decomposition Methods for Mortar Finite Element Discretizations of Plate Problems , 2001, SIAM J. Numer. Anal..

[30]  P. G. Ciarlet,et al.  Basic error estimates for elliptic problems , 1991 .

[31]  C. Bernardi,et al.  A New Nonconforming Approach to Domain Decomposition : The Mortar Element Method , 1994 .

[32]  Wolfgang Dahmen,et al.  A Multigrid Algorithm for the Mortar Finite Element Method , 1999, SIAM J. Numer. Anal..

[33]  Xuejun Zhang,et al.  Studies in Domain Decomposition: Multi-level Methods and the Biharmonic Dirichlet Problem , 1991 .

[34]  Wlodzimierz Proskurowski,et al.  A FETI-DP Preconditioner with A Special Scaling for Mortar Discretization of Elliptic Problems with Discontinuous Coefficients , 2006, SIAM J. Numer. Anal..

[35]  Olof B. Widlund,et al.  A FETI - DP Method for a Mortar Discretization of Elliptic Problems , 2002 .

[36]  C. Farhat,et al.  A Scalable Substructuring Method By Lagrange Multipliers For Plate Bending Problems , 1996 .