A Balancing Domain Decomposition by Constraints (BDDC) preconditioner for Isogeometric Analysis of scalar elliptic problems is constructed and analyzed by introducing appropriate discrete norms. A main result of this work is the proof that the proposed isogeometric BDDC preconditioner is scalable in the number of subdomains and quasi-optimal in the ratio of subdomain and element sizes. Another main result is the numerical validation of the theoretical convergence rate estimates by carrying out several two- and three-dimensional tests on serial and parallel computers. These numerical experiments also illustrate the preconditioner performance with respect to the polynomial degree and the regularity of the NURBS basis functions, as well as its robustness with respect to discontinuities of the coefficient of the elliptic problem across subdomain boundaries.

BDDC preconditioners for isogeometric analysis / L. Beirao da Veiga, D. Cho, L. Pavarino, S. Scacchi. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 23:6(2013 Jun), pp. 1099-1142.

BDDC preconditioners for isogeometric analysis

L. Beirao da Veiga
Primo
;
D. Cho
;
L. Pavarino
Penultimo
;
S. Scacchi
Ultimo
2013

Abstract

A Balancing Domain Decomposition by Constraints (BDDC) preconditioner for Isogeometric Analysis of scalar elliptic problems is constructed and analyzed by introducing appropriate discrete norms. A main result of this work is the proof that the proposed isogeometric BDDC preconditioner is scalable in the number of subdomains and quasi-optimal in the ratio of subdomain and element sizes. Another main result is the numerical validation of the theoretical convergence rate estimates by carrying out several two- and three-dimensional tests on serial and parallel computers. These numerical experiments also illustrate the preconditioner performance with respect to the polynomial degree and the regularity of the NURBS basis functions, as well as its robustness with respect to discontinuities of the coefficient of the elliptic problem across subdomain boundaries.
Dual-primal methods; BDDC; FETI-DP; scalable preconditioners; Isogeometric Analysis; finite elements; NURBS
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/2434/224700
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