Summary: NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Numer. Linear Algebra Appl. 2009; 00:1­19 Prepared using nlaauth.cls [Version: 2002/09/18 v1.02]
Robust multigrid preconditioners for the high-contrast
biharmonic plate equation
Burak Aksoylu1,2, Zuhal Yeter2
1 TOBB University of Economics and Technology, Department of Mathematics, Ankara, 06560, Turkey
2 Louisiana State University, Department of Mathematics, Baton Rouge, LA 70803, USA
SUMMARY
We study the high-contrast biharmonic plate equation with HCT discretization. We construct a
preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the
preconditioner proposed by Aksoylu et al. (2008, Comput. Vis. Sci. 11, pp. 319­331). By extending
the devised singular perturbation analysis from linear finite element discretization to the above
discretization, we prove and numerically demonstrate the robustness of the preconditioner. Therefore,
we accomplish a desirable preconditioning design goal by using the same family of preconditioners
to solve elliptic family of PDEs with varying discretizations. We also present a strategy on how
to generalize the proposed preconditioner to cover high-contrast elliptic PDEs of order 2k, k > 2.
Moreover, we prove a fundamental qualitative property of solution of the high-contrast biharmonic
plate equation. Namely, the solution over the highly-bending island becomes a linear polynomial
asymptotically. The effectiveness of our preconditioner is largely due to the integration of this
qualitative understanding of the underlying PDE into its construction. Copyright c 2009 John

Source: Aksoylu, Burak - Center for Computation and Technology & Department of Mathematics, Louisiana State University

Collections: Computer Technologies and Information Sciences