The discrete systems generated by spectral or hp-version finite elements are much more ill-conditioned than the ones generated by standard low-order finite elements or finite differences. This paper focuses on spectral elements based on Gauss-Lobatto-Legendre (GLL) quadrature and the construction of primal and dual non-overlapping domain decomposition methods belonging to the family of Balancing Domain Decomposition methods by Constraints (BDDC) and Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) algorithms. New results are presented for the spectral multi-element case and also for inexact FETI-DP methods for spectral elements in the plane. Theoretical convergence estimates show that these methods have a convergence rate independent of the number of subdomains and coefficient jumps of the elliptic operator, while there is only a polylogarithmic dependence on the spectral degree p and the ratio H/h of subdomain and element sizes. Parallel numerical experiments on a Linux cluster confirm these results for tests with spectral degree up to p = 32, thousands of subdomains and coefficient jumps up to 8 orders of magnitude.

Spectral element FETI-DP and BDDC preconditioners with multielement subdomains / A. Klawonn, L. F. Pavarino, O. Rheinbach. - In: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. - ISSN 0045-7825. - 198:3-4(2008), pp. 511-523.

Spectral element FETI-DP and BDDC preconditioners with multielement subdomains

L. F. Pavarino
Secondo
;
2008

Abstract

The discrete systems generated by spectral or hp-version finite elements are much more ill-conditioned than the ones generated by standard low-order finite elements or finite differences. This paper focuses on spectral elements based on Gauss-Lobatto-Legendre (GLL) quadrature and the construction of primal and dual non-overlapping domain decomposition methods belonging to the family of Balancing Domain Decomposition methods by Constraints (BDDC) and Dual-Primal Finite Element Tearing and Interconnecting (FETI-DP) algorithms. New results are presented for the spectral multi-element case and also for inexact FETI-DP methods for spectral elements in the plane. Theoretical convergence estimates show that these methods have a convergence rate independent of the number of subdomains and coefficient jumps of the elliptic operator, while there is only a polylogarithmic dependence on the spectral degree p and the ratio H/h of subdomain and element sizes. Parallel numerical experiments on a Linux cluster confirm these results for tests with spectral degree up to p = 32, thousands of subdomains and coefficient jumps up to 8 orders of magnitude.
BDDC; Domain decomposition methods; Elasticity; FETI; Lagrange multipliers; Preconditioners; Spectral elements
Settore MAT/08 - Analisi Numerica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/53920
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