BDDC PRECONDITIONERS FOR ISOGEOMETRIC ANALYSIS

被引：58

作者：

da Veiga, L. Beirao ^{[1
]}

Cho, D. ^{[1
,2
]}

Pavarino, L. F. ^{[1
]}

Scacchi, S. ^{[1
]}

机构：

[1] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Dongguk Univ, Dept Math, Seoul 100715, South Korea

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2013年 / 23卷 / 06期

关键词：

Dual-primal methods; BDDC; FETI-DP; scalable preconditioners; Isogeometric Analysis; finite elements; NURBS; SPECTRAL ELEMENT DISCRETIZATIONS; FETI-DP; FINITE-ELEMENTS; DOMAIN DECOMPOSITION; ENERGY MINIMIZATION; DIMENSIONS; NURBS; REFINEMENT; ELASTICITY; APPROXIMATIONS;

D O I：

10.1142/S0218202513500048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1099 / 1142

页数：44

共 45 条

[1] [Anonymous], 2006, MATH MOD METH APPL S
[2] [Anonymous], 2004, COMPUTATIONAL MATH
[3] ISOGEOMETRIC COLLOCATION METHODS
Auricchio, F.
Da Veiga, L. Beirao
Hughes, T. J. R.
Reali, A.
Sangalli, G.
[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2010, 20 (11) : 2075 - 2107
[4] The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations
Auricchio, F.
da Veiga, L. Beirao
Lovadina, C.
Reali, A.
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (5-8) : 314 - 323
[5] Isogeometric fluid-structure interaction: theory, algorithms, and computations
Bazilevs, Y.
Calo, V. M.
Hughes, T. J. R.
Zhang, Y.
[J]. COMPUTATIONAL MECHANICS, 2008, 43 (01) : 3 - 37
[6] Isogeometric analysis using T-splines
Bazilevs, Y.
Calo, V. M.
Cottrell, J. A.
Evans, J. A.
Hughes, T. J. R.
Lipton, S.
Scott, M. A.
Sederberg, T. W.
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (5-8) : 229 - 263
[7] A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM
Benson, D. J.
Bazilevs, Y.
De Luycker, E.
Hsu, M. -C.
Scott, M.
Hughes, T. J. R.
Belytschko, T.
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2010, 83 (06) : 765 - 785
[8] Isogeometric shell analysis: The Reissner-Mindlin shell
Benson, D. J.
Bazilevs, Y.
Hsu, M. C.
Hughes, T. J. R.
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (5-8) : 276 - 289
[9] BDDC and FETI-DP without matrices or vectors
Brenner, Susanne C.
Sung, Li-Yeng
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (08) : 1429 - 1435
[10] ISOGEOMETRIC DISCRETE DIFFERENTIAL FORMS IN THREE DIMENSIONS
Buffa, A.
Rivas, J.
Sangalli, G.
Vazquez, R.
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2011, 49 (02) : 818 - 844

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