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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Block FETI–DP/BDDC preconditioners for mixed isogeometric discretizations of three-dimensional almost incompressible elasticity
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by O. B. Widlund, S. Zampini, S. Scacchi and L. F. Pavarino HTML | PDF
Math. Comp. 90 (2021), 1773-1797 Request permission


A block FETI–DP/BDDC preconditioner for mixed formulations of almost incompressible elasticity is constructed and analyzed; FETI–DP (Finite Element Tearing and Interconnecting Dual-Primal) and BDDC (Balancing Domain Decomposition by Constraints) are two very successful domain decomposition algorithms for a variety of elliptic problems. The saddle point problems of the mixed problems are discretized with mixed isogeometric analysis with continuous pressure fields. As in previous work by Tu and Li (2015) for finite element discretizations of the incompressible Stokes system, the proposed preconditioner is applied to a reduced positive definite system involving only the pressure interface variable and the Lagrange multiplier of the FETI–DP algorithm. In this work, we extend the theory to a wider class of saddle point problems and we propose a novel block-preconditioning strategy, which consists in using BDDC with deluxe scaling for the interface pressure block as well as deluxe scaling for the FETI–DP preconditioner for the Lagrange multiplier block. A convergence rate analysis is presented with a condition number bound for the preconditioned operator which depends on the inf-sup parameter of the fully assembled problem and the condition number of a closely related BDDC algorithm for compressible elasticity. This bound is scalable in the number of subdomains, poly-logarithmic in the ratio of subdomain and element sizes, and robust with respect to material incompressibility. Parallel numerical experiments validate the theory, demonstrate robustness in the presence of discontinuities of the Lamé parameters, and indicate how the rate of convergence varies with respect to the spline polynomial degree and regularity and the deformation of the domain.
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Additional Information
  • O. B. Widlund
  • Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
  • MR Author ID: 182600
  • Email:
  • S. Zampini
  • Affiliation: Extreme Computing Research Center, King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
  • MR Author ID: 923734
  • ORCID: 0000-0002-0435-0433
  • Email:
  • S. Scacchi
  • Affiliation: Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy
  • MR Author ID: 828985
  • ORCID: 0000-0001-6011-784X
  • Email:
  • L. F. Pavarino
  • Affiliation: Dipartimento di Matematica, Università degli Studi di Pavia, Via Ferrata 5, 27100 Pavia, Italy
  • MR Author ID: 291739
  • Email:
  • Received by editor(s): April 9, 2020
  • Received by editor(s) in revised form: September 23, 2020
  • Published electronically: March 24, 2021
  • Additional Notes: The first author has been supported by the National Science Foundation Grant DMS-1522736. The third author was supported by grants of Istituto Nazionale di Alta Matematica (INDAM-GNCS). The fourth author was partially supported by the European Research Council through the FP7 Ideas Consolidator Grant HIGEOM n. 616563, by the Italian Ministry of Education, University and Research (MIUR) through the “Dipartimenti di Eccellenza Program 2018-22 - Dept. of Mathematics, University of Pavia”, and by the Istituto Nazionale di Alta Matematica (INdAM - GNCS), Italy
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 90 (2021), 1773-1797
  • MSC (2020): Primary 65F08, 65N30, 65N35, 65N55
  • DOI:
  • MathSciNet review: 4273115