Forschungsbericht 2007



Projektionsverfahren für dünn besetzte nichtlineare Eigenwertaufgaben

Institut: Numerische Simulation
Projektleitung: Prof.Dr.rer.nat. Heinrich Voß
Stellvertretende Projektleitung: Prof.Dr.rer.nat. Wolfgang Mackens
Mitarbeiter/innen: Dipl.-Math. Lada Mazurenko , Dipl.-Ing. Marta Betcke
Projektnummer: E.4-13.022
Laufzeit: 01.01.2002 - 31.12.2010
Finanzierung: TUHH, DFG


 

Für dünn besetzte lineare Eigenwertaufgaben sind iterative Projektionsverfahren

wie das Lanczos Verfahren, Arnoldi Verfahren oder Jacobi-Davidson Verfahren sehr

erfolgreich. Hierbei wird eine Basis des Raumes, auf den das Ausgangsproblem projiziert

wird, im Laufe des Verfahren bestimmt und gleichzeitig eine Matrix kleiner Dimension

erzeugt, die das projizierte Problem repräsentiert. Auf diese kann dann ein

Standardverfahren angewandt werden, um Näherungslösungen zu erhalten.

Ziel dieses Projektes ist es, eine analoge Vorgehensweise auch für nichtlineare

Eigenwertaufgaben zu entwickeln.

Weitere Informationen zu diesem Forschungsprojekt können Sie hier bekommen.

 

Publikationen
  • 4-13.069V

    Timo Betcke, Heinrich Voss: A Jacobi-Davidson type projection method for nonlinear eigenvalue problems. Future Generation Computer Systems, 20, pp. 363--372 (2004)

  • 4-13.070V

    Heinrich Voss: A rational spectral problem in fluid-solid vibration.Electronic Transactions on Numerical Analysis 16, pp. 94--106 (2003)

  • 4-13.073V

    Heinrich Voss: A Projection Method for a Rational Eigenvalue Problem in Fluid-Structure Interaction. pp. 403--411 in P.M.A. Sloot, C.J.K. Tan, J.J. Dongarra, A.G. Hoekstra (eds.), Computational Science 2002, LNCS 2330, Springer Verlag, Berlin 2002

  • 4-13.074V

    Heinrich Voss: Solving a Rational Eigenvalue Problem in Fluid-Structure Interaction. pp. 179--188 in C.A. Brebbia, P. Meli, A. Zanasi (eds.), Applications of High-Performance Computing in Engineering VII. WIT Press, Southampton 2002

  • 4-13.075V

    Heinrich Voss: Variational Characterization of Eigenvalues of Nonlinear Eigenproblems. pp. 379--383 in M. Kocandrlova, V. Kelar (eds.), Proceedings of the International Conference on Mathematical and Computer Modelling in Science and Engineering Czech Technical University in Prague 2003

  • 4-13.078V

    Heinrich Voss: An Arnoldi type projection method for nonlinear symmetric eigenproblems. Proc. Appl. Math. 3, pp. 555--556 (2003)

  • 4-13.079V

    Heinrich Voss: An Arnoldi method for nonlinear eigenvalue problems. BIT Numerical Mathematics 44, 387--401 (2004)

  • 4-13.084V

    Elias Jarlebring, Heinrich Voss: Rational Krylov for nonlinear eigenproblems, an iterative projection method. Applications of Mathematics 50, 543--554 (2005)

  • 4-13.085V

    Heinrich Voss: Iterative projection methods for sparse nonlinear eigenproblems. Proc. Appl. Math. Mech. 4, 722--725 (2004)

  • 4-13.086V

    Marta Markiewicz, Heinrich Voss: Computing Interior Eigenvalues of Conservative Gyroscopic Problems. Proc. Appl. Math. Mech. 4, 674--675 (2004)

  • 4-13.088V

    Heinrich Voss: An Arnoldi method for nonlinear symmetric eigenvalue problems. Online Proceedings, SIAM Conference on Applied Linear Algebra, Williamsburg 2003. http://www.siam.org/meetings/la03/proceedings/VossH.pdf

  • 4-13.090V

    Heinrich Voss: A Jacobi-Davidson method for nonlinear eigenproblems. pp. 34--41 in M. Buback, G.D. van Albada, P.M.A. Sloot, J.J. Dongarra (eds.), Computational Science - ICCS 2004. 4th International Conference, Kraków, Poland, 2004, Proceedings, Part II, Lecture Notes in Computer Science 3037, Springer Verlag, Berlin, Heidelberg, New York 2004

  • 4-13.092V

    Heinrich Voss: A Jacobi-Davidson type projection method for general nonlinear eigenproblems. in B.H.V. Topping, S.A. Mota Soares (eds.), Proceedings (CD-Rom) of The Seventh International Conference on Computational Structures Technology, Lisbon, Portugal 2004, ISBN 0-948749-94-6

  • 4-13.093V

    Heinrich Voss: Eigenvibrations of a plate with elastically attached loads in P. Neittaanmäki, T. Rossi, S. Korotov, E. Onate, J. Periaux, D. Knärzer (eds.). Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering. ECCOMAS 2004, Jyväskylä, Finnland 2004, ISBN 951-39-1869-6

  • 4-13.111V

    Heinrich Voss: Numerical methods for sparse nonlinear eigenproblems.pp. 133 -- 160 in I. Marek, J. Holenda (eds.), Proceedings of the XV-th Summer School on Software and Algorithms of Numerical Mathematics, Hejnice, 2003, University of West Bohemia, Pilsen, Czech Republic, 2004

  • 4-13.112V

    Volker Mehrmann, Heinrich Voss: Nonlinear eigenvalue problems: A challenge for modern eigenvalue methods. GAMM-Mitt. 27, 121--152 (2004)

  • 4-13.113V

    Marta Markiewicz, Heinrich Voss: A local restart procedure for iterative projection methods for nonlinear symmetric eigenproblems. pp. 212--221 in A. Handlovicova, Z. Kriva, K. Mikula, D. Sevovic (eds.), Algorithmy 2005, 17th Conference on Scientific Computing Vysoke Tatry - Podbanske, Slovakia 2005. Slovak University of Technology, Bratislava 2005

  • 4-13.115V

    Heinrich Voss: Electron energy level calculation for a three dimensional quantum dot pp. 586 -- 589 in T. Simos, G. Maroulis (eds.), Advances in Computational Methods in Sciences and Engineering 2005, Lecture Series in Computer and Computational Sciences, Vol. 4, Brill Academic Publishers, Leiden, the Netherlands 2005

  • 4-13.118V

    Heinrich Voss: Numerical simulation of a three dimensional quantum dot. Proc.Appl.Math.Mech. 5, 783 -- 784 (2005)

  • 4-13.119V

    Heinrich Voss: Projection methods for nonlinear sparse eigenvalue problems Annals of the European Academy of Sciences, 152 -- 183 (2005)

  • 4-13.120V

    Heinrich Voss: Numerical calculation of the electronic structure for three-dimensional quantum dots. Comput. Phys. Comm. 174, 441 -- 446 (2006)

  • 4-13.121V

    Marta Markiewicz, Heinrich Voss: Electronic States in Three Dimensional Quantum Dot/Wetting Layer Structures pp. 684 -- 693 in M. Gavrilova et al. (eds.), Computational Science and its Applications -- ICCSA 2006, Lecture Notes in Computer Science 3980, Springer Verlag, Berlin, Heidelberg, New York 2006

  • 4-13.124V

    Marta Markiewicz, Heinrich Voss: Electronic States in Three Dimensional Quantum Dot/Wetting Layer Structures on CD--ROM Proceedings of Computational Science and its Applications -- ICCSA 2006, Glasgow, UK, May 2006

  • 4-13.125V

    Heinrich Voss: Iterative projection methods for computing relevant energy states of a quantum dot. J. Comput. Phys. 217, 824 -- 833 (2006)

  • 4-13.127V

    Heinrich Voss: A Jacobi--Davidson method for nonlinear and nonsymmetric eigenproblems. Computers & Structures 85, pp. 1284--1292 (2007)

  • 4-13.133V

    Marta Betcke and Heinrich Voss: Electronic states of Quantum Dots. Report 85, Institut für Numerische Simulation, TU Hamburg-Harburg 2004

  • 4-13.135V

    Marta Betcke and Heinrich Voss: Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin--orbit splitting. Applications of Mathematics 52, pp. 267--284 (2007)

  • 4-13.143V

    Heinrich Voss: Robust expansion of subspaces in iterative projection methods for large eigenvalue problems. Proc. Appl. Math. Mech. 7, pp. 1021001--1021002 (2007)

  • 4-13.146D

    Marta Betcke: Iterative Projection Methods for Symmetric Nonlinear Eigenvalue Problems with Applications