Robust semi-coarsening multilevel preconditioning of biquadratic FEM systems

• Autorzy: Maria Lymbery , Svetozar Margenov
• Języki publikacji: EN

Abstrakty

EN

While a large amount of papers are dealing with robust multilevel methods and algorithms for linear FEM elliptic systems, the related higher order FEM problems are much less studied. Moreover, we know that the standard hierarchical basis two-level splittings deteriorate for strongly anisotropic problems. A first robust multilevel preconditioner for higher order FEM systems obtained after discretizations of elliptic problems with an anisotropic diffusion tensor is presented in this paper. We study the behavior of the constant in the strengthened CBS inequality for semi-coarsening mesh refinement which is a quality measure for hierarchical two-level splittings of the considered biquadratic FEM stiffness matrices. The presented new theoretical estimates are confirmed by numerically computed CBS constants for a rich set of parameters (coarsening factor and anisotropy ratio). In the paper we consider also the problem of solving efficiently systems with the pivot block matrices arising in the hierarchical basis two-level splittings. Combining the proven uniform estimates with the theory of the Algebraic MultiLevel Iteration (AMLI) methods we obtain an optimal order multilevel algorithm whose total computational cost is proportional to the size of the discrete problem with a proportionality constant independent of the anisotropy ratio.

Słowa kluczowe

EN

Biquadratic finite elements; Multilevel methods; Robust preconditioning

Kategorie tematyczne

• 65N22: Solution of discretized equations
• 65F08: Preconditioners for iterative methods

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 1
• Strony: 357-369

Daty

wydano

2012-02-01

online

2011-12-09

Twórcy

autor

Maria Lymbery

• Bulgarian Academy of Sciences

autor

Svetozar Margenov

• Bulgarian Academy of Sciences

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-011-0082-3