Spezialvorlesung Numerische Mathematik (Isogeometric Analysis) 2VO + 1UE
Lecturer (lecture): Stefan TakacsLecturer (tutorial): Thomas Takacs
Time and Room (for lecture and tutorial):
- Thu at 08:30 - 10:00 in S2 120
- Fri at 12:00 - 13:30 in S2 054
Exam: presentation or oral exam
Contents:
References | ||
Thu 20 Oct | Lecture 1: Introduction, B-splines, NURBS | [1,2] |
Fri 21 Oct | Lecture 2: IgA principle, Approximation error estimates | [1,3] |
Thu 27 Oct | Lecture 3: Approximation error estimates | [1,3] |
Fri 28 Oct | Lecture 4: p-robust approximation error estimates | [1,4,5] |
Thu 3 Nov | Lecture 5: p-robust approximation error estimates, Inverse estimates | [5,6,7] |
Fri 4 Nov | Lecture 6: Multi-patch IgA | [8,9] |
Thu 10 Nov | Lecture 7: Multi-patch IgA, T-splines | [8,9,10] |
Fri 11 Nov | Lecture 8: T-splines, (T)HB-splines | [10,11] |
Thu 17 Nov | Lecture 9: Galerkin and collocation methods, Assembling | [12,13,14] |
Fri 18 Nov | Lecture 10: Assembling | [14,15] |
Thu 24 Nov | Lecture 11: Assembling, Stokes | [16,1] |
Fri 25 Nov | Lecture 12: Stokes, Preconditioners | [1,17] |
Thu 15 Dec | Lecture 13: Multigrid | [18,19,20,21] |
Fri 16 Dec | Lecture 14: Overlapping Schwarz, IETI | [1,22,23,24,25] |
Thu 12 Jan | A. Fohler: Maxwell | |
J. Sogn: Stokes | ||
Fri 13 Jan | N. Engleitner: THB splines | |
F. Scholz: Low-rank assembling | ||
Thu 19 Jan | B. Endtmayer: local error estimates | |
A. Schafelner: T-splines | ||
Fri 20 Jan | R. Schneckenleitner: High order FEM vs. IgA | |
M. Hauer: web-splines | ||
Thu 26 Jan | L. Mitter: IETI (Part 1) | |
C. Hofer: IETI (Part 2) | ||
Fri 27 Jan | D. Jodlbauer: Multipatch DG (Part 1) | |
A. Seiler: Multipatch DG (Part 2) |
Lecture notes:
- The lecture notes are available in KUSSS.
Literature:
- [1]
- L. Beirao da Veiga, A. Buffa, G. Sangalli, R. Vazquez. Mathematical analysis of variational isogeometric methods. Acta Numerica, 23, pp. 157-287, 2014.
- [2]
- T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. CMAME, 194 (39-41), pp. 4135-4195, 2005. (DOI:10.1016/j.cma.2004.10.008)
- [3]
- L. Schumaker. Spline functions. Cambridge University Press. 1981. (Library)
- [4]
- L. Beirao da Veiga, A. Buffa, J. Rivas, and G. Sangalli. Some estimates for h-p-k-refinement in isogeometric analysis. Numerische Mathematik, 118 (2), pp. 271-305, 2011. (DOI:10.1007/s00211-010-0338-z)
- [5]
- S. Takacs and T. Takacs. Approximation error estimates and inverse inequalities for B-splines of maximum smoothness. M3AS, 26 (7), pp. 1411-1445, 2016. (arXiv:1502.03733)
- [6]
- C. Schwab. p and hp Finite Element Methods: Theory and applications in solid and fluid mechanics. Clarendon Press. 1998. (Library)
- [7]
- C. Koutschan, M. Neumüller, S. Radu. Inverse inequality estimates with Symbolic Computation. Advances in Applied Mathematics, 80, pp. 1-23, 2016. (DOI:10.1016/j.aam.2016.04.005)
- [8]
- G. Sangalli, T. Takacs, and R. Vazquez. Unstructured spline spaces for isogeometric analysis based on spline manifolds. CAGD, 47, pp. 61-82, 2016. (DOI:10.1016/j.cagd.2016.05.004)
- [9]
- A. Collin, G. Sangalli, and T. Takacs. Analysis-suitable G1 multi-patch parametrizations for C1 isogeometric spaces. CAGD, 47, pp. 93-113, 2016. (DOI:10.1016/j.cagd.2016.05.009)
- [10]
- L. Beirao da Veiga, A. Buffa, G. Sangalli, and R. Vazquez. Analysis-suitable T-splines of arbitrary degree: definition, linear independence and approximation properties. M3AS, 23 (11), pp. 1979-2003, 2013. (http://www-dimat.unipv.it/sangalli/AS_DC_high_order.pdf)
- [11]
- C. Giannelli, B. Jüttler, H. Speleers. THB-splines: The truncated basis for hierarchical splines. CAGD, 29 (7), pp. 485-498, 2012. (DOI:10.1016/j.cagd.2012.03.025)
- [12]
- F. Auricchio, L. Beirao da Veiga, T.J.R. Hughes, A. Reali, G. Sangalli. Isogeometric Collocation Methods. M3AS, 20 (11), pp. 2075 - 2107, 2010. (citeseerx.ist.psu.edu)
- [13]
- R. Hoppe. Finite element methods, chapter 4. (https://www.math.uh.edu/~rohop/spring_05/)
- [14]
- P. Antolin, A. Buffa, F. Calabro, M. Martinelli, G. Sangalli. Efficient matrix computation for tensor-product isogeometric analysis: The use of sum factorization. CMAME, 285, pp. 817-828. 2015. (DOI:10.1016/j.cma.2014.12.013)
- [15]
- F. Calabro, G. Sangalli, M. Tani. Fast formation of isogeonetric Galerkin matrices by weighted quadrature. CMAME, in press. (DOI:10.1016/j.cma.2016.09.013)
- [16]
- A. Mantzaflaris, B. Jüttler, B. N. Khoromskij, U. Langer. Matrix Generation in Isogeometric Analysis by Low Rank Tensor Approximation. Curves and Surfaces, pp 321-340. 2015. (DOI:10.1007/978-3-319-22804-4_24)
- [17]
- G. Sangalli and M. Tani. Isogeometric Preconditioners Based on Fast Solvers for the Sylvester Equation. SIAM J. Sci. Comput., 38(6), pp 3644-3671. 2016. (DOI:10.1137/16M1062788)
- [18]
- W. Hackbusch Multi-Grid Methods and Applications. Springer. 2003. (Library)
- [19]
- C. Hofreither, B. Jüttler, G. Kiss, W. Zulehner. Multigrid methods for isogeometric analysis with THB-Splines. CMAME, 308, pp. 96-112. 2016. (DOI:10.1016/j.cma.2016.05.005)
- [20]
- C. Hofreither, S. Takacs, W. Zulehner. A Robust Multigrid Method for Isogeometric Analysis using Boundary Correction. CMAME. Available online. 2016. (DOI:10.1016/j.cma.2016.04.003)
- [21]
- C. Hofreither, S. Takacs. Robust Multigrid for Isogeometric Analysis Based on Stable Splittings of Spline Spaces. Submitted. 2016. (arXiv:1607.05035)
- [22]
- L. Beirao da Veiga, D. Cho, L. Pavarino, S. Scacchi. Overlapping Schwarz Methods for Isogeometric Analysis. SINUM, 50(3), pp. 1394-141. 2012. (DOI:10.1137/110833476)
- [23]
- M. Bercovier, I. Soloveichi. Overlapping non Matching Meshes Domain Decomposition Method in Isogeometric Analysis. Submitted. 2015. (arXiv:1502.03756)
- [24]
- S. Kleiss, C. Pechstein, B. Jüttler, S. Tomar. IETI - Isogeometric Tearing and Interconnecting. CMAME, 247-248, pp. 201-215. 2012. (DOI:10.1016/j.cma.2012.08.007)
- [25]
- M. Gander, G. Wanner. The Origins of the Alternating Schwarz Method. Lecture Notes in Computational Science and Engineering, 98, pp 487-495. 2014. (https://www.unige.ch/~gander/Preprints/gander_mini_11.pdf)