Seminar on Numerical Methods | letzte Änderung: 2021-10-03 |
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Seminar on Numerical Methods
Schwarz' Methods for Solving Partial Differential Equations
(Course Id 327.050, 2 hours per week, semester 5)Supervisors: a.Univ.-Prof. Dr. Helmut Gfrerer
o.Univ.-Prof. Dr. Ulrich Langer
a.Univ.-Prof. Dr. Walter Zulehner
Univ.-Prof. Dr. Ludmil Zikatanov
Start of the seminar: Tue, 2008-10-14, 13:45 - 15:15 Uhr, Room: T 112
Time, room, seminar, student, supervisor:
| Tu, 2008-10-14 | 13:45 - 15:15 Room: T 112 | Introduction | ||
| Tu, 2008-10-21 | 13:45 - 15:15 Room: T 112 | Consultation | ||
| Tu, 2008-10-28 | 13:45 - 15:15 Room: T 112 | Seminar 01 | Kowalska | Gfrerer |
| Tu, 2008-11-04 | 13:45 - 15:15 Room: T 112 | Seminar 02 | Wandl | Langer |
| Tu, 2008-11-11 | 13:45 - 15:15 Room: T 112 | Seminar 03 | Moussa | Zulehner |
| Tu, 2008-11-18 | 13:45 - 15:15 Room: T 112 | Seminar 04 | Okyere | Langer |
| Tu, 2008-11-25 | 13:45 - 15:15 Raum: T 112 | Seminar 05 | Wu, Zhou | Gfrerer |
| Tu, 2008-12-02 | 13:45 - 15:15 Raum: T 112 | Seminar 06 | Akinwumi | Zulehner |
| Tu, 2008-12-09 | 13:45 - 15:15 Raum: T 112 | Seminar 07 | Akindeinde | Langer |
| Tu, 2008-12-16 | 13:45 - 15:15 Raum: T 112 | Seminar 08 | Burger, Kolmbauer | Gfrerer |
| Tu, 2009-01-13 | 13:45 - 15:15 Room: T 112 | Seminar 09 | Thien, Pandey | Zulehner |
| Tu, 2009-01-20 | 13:45 - 15:15 Room: T 112 | Seminar 10 | A. Langer | Zikatanov, U. Langer |
| Tu, 2009-01-27 | 13:45 - 15:15 Room: T 112 | Seminar 11 | Purrucker | Zikatanov, Zulehner |
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Seminar Topics | up |
| Seminar 01: | 28.10.2008 Classical Schwarz Algorithm and its convergence via maximum principle Literature: [1]; [3], Section 1 and 2 Supervisor: Helmut Gfrerer Student: Monika Kowalska |
| Seminar 02: | 04.11.2008 Variational interpretation of the Alternating Schwarz Method Literature: [2], Section 1.1 - 1.2, [5], pp. 122-126 Supervisor: Ulrich Langer Student: Sabrina Wandl |
| Seminar 03: | 11.11.2008 Extension to more subdomains Literature: [2], Section 1.4 Supervisor: Walter Zulehner Student: Sanaa Moussa |
| Seminar 04: | 18.11.2008 Robin-Robin nonoverlapping DDM Literature: [4] Supervisor: Ulrich Langer Student: Eric Okyere |
| Seminar 05: | 25.11.2008 Multi-domain formulations Literature: [6], Sections 1.1 und 1.2 Supervisor: Helmut Gfrerer Student: Zhen Wu und Yao Zhou |
| Seminar 06: | 02.12.2008 Iterative substucturing methods based on transmission conditions at the interface Literature: [6], Section 1.3 Supervisor: Walter Zulehner Student: Segun Michael Akinwumi |
| Seminar 07: | 09.12.2008 Generalizations Literature: [6], Section 1.4 Supervisor: Ulrich Langer Student: Saheed Ojo Akindeinde |
| Seminar 08: | 16.12.2008 Abstract Theory of Schwarz Methods: I. Schwarz Methods [7], Section 2.2, pp. 35-39 II. Convergence Theory (ASM), [7], Section 2.3, pp. 39-43 Literature: [7], Chapter 2 Supervisor: Helmut Gfrerer Student: Robert Burger (I), Michael Kolmbauer (II) |
| Seminar 09: | 13.01.2008 Abstract Theory of Schwarz Methods: III. Convergence Theory (MSM), [7], Section 2.3, pp. 44-46 IV. Aditional Results: [7], Section 2.4ff, pp. 46-53 Literature: [7], Chapter 2 Supervisor: Walter Zulehner Student: Tuan Thien Nguyen (III), Ankur Pandey (IV) |
| Seminar 10: | 20.01.2009 Subspace Correction Methods I Literature: [8] + additional references [9] - [12] Supervisor: Ludmil Zikatanov, Ulrich Langer Student: Andreas Langer |
| Seminar 11: | 27.01.2009 Subspace Correction Methods II Literature: [8] + additional references [9] - [12] Supervisor: Ludmil Zikatanov, Walter Zulehner Student: Martin Purrucker |
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Literature | up |
[1] Schwarz, H.A.: Über einen Grenzübergang durch alternierendes Verfahren. Vierteljahresschriften der Naturforschenden Gesellschaft in Zürich. 15 (1870), 133 - 143.
[2] Lions, P.L.: On the Schwarz Alternating Method I. Proceedings of the DD1, 1988, 1-42.
[3] Lions, P.L.: On the Schwarz Alternating Method II. Proceedings of the DD2, 1989, 47-70.
[4] Lions, P.L.: On the Schwarz Alternating Method III. Proceedings of the DD3, 1990, 202-223.
[5] Nepomnyaschikh, S.: Domain Decomposition Methods. In "Lectures on Advanced Computational Methods in Mechanics" (edited by J. Kraus and U. Langer), Radon Series on Computational and Applied Mathematics, v. 1, 89-159.
[6] Quarteroni A., Valli A.: Domain Decomposition Methods for Partial Differential Equation. Oxford Science Publications, Oxford, 1999.
[7] Toselli A., Widlund O.: Domain Decomposition Methods - Algorithms and Theory. Springer-Verlag, Berlin, Heidelberg, New York, 2005.
[8] Zikatanov L.: Subspace Correction Methods (Private Communication).
[9] Xu J., Zikatanov L.: The method of alternating pro jections and the method of subspace corrections in Hilbert space. J. Amer. Math. Soc., 15(3):573–597 (electronic), 2002.
[10] Zikatanov L.: Two-sided bounds on the convergence rate of two-level methods. Numer. Linear Algebra Appl., 15(5):439–454, 2008.
[11] Xu J.: Iterative methods by space decomposition and subspace correction. SIAM Rev., 34(4):581–613, 1992.
[12] Bramble J.H., Pasciak J.E., Wang J.P., and Xu J.: Convergence estimates for multigrid algorithms without regularity assumptions. Math. Comp., 57(195):23–45, 1991.
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Participants | up |
Akindeinde Saheed Ojo
Akinwumi Segun Michael
Burger Robert
Kolmbauer Michael
Kowalska Monika
Langer Andreas
Nguyen Tuan Thien
Okyere Eric
Pandey Ankur
Purrucker Martin
Sanaa Moussa
Wandl Sabrina
Wu Zhen
Zhou Yao
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General Remarks | up |
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DD-Links | up |
