Spezialvorlesung Numerische Mathematik (Isogeometric Analysis) 2VO + 1UE

Lecturer (lecture): Stefan Takacs
Lecturer (tutorial): Thomas Takacs

Time and Room (for lecture and tutorial): Language: EN

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:

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)