Kolloquium der Arbeitsgruppe Modellierung • Numerik • Differentialgleichungen
||Alle Professoren der|
Arbeitsgruppe Modellierung • Numerik • Differentialgleichungen
|Koordination: ||Prof. Dr.
|Termine: ||Di 16-18 Uhr in MA 313
und nach Vereinbarung|
|Inhalt: ||Vorträge von
Gästen und Mitarbeitern zu aktuellen
Uhr||MA 313||Avi Berman|
(The Technion, Haifa)
|Diagonal stability and completely positive
(U of Kansas)
|Conditioning of Finite Element Equations with
Lennard Kamenski (University of Kansas)
Conditioning of Finite Element Equations
with Anisotropic Meshes
Dienstag, den 27.09.2011, 16.15 Uhr in MA 313 Abstract:
In n >= 2 dimensions, it has been proven by Bank and Scott that
the condition number of finite element equations does not degrade
significantly on adaptive meshes if the mesh remains locally
quasi-uniform and an appropriate scaling of the resulting system is
In this talk, I will present a generalization of the result by Bank
and Scott. The developed bound on the condition number is valid for
general meshes, without any assumptions on the shape of mesh elements.
As in isotropic case, an appropriately chosen, mesh-dependent diagonal
scaling can be used to significantly improve the conditioning of the
resulting linear system.
An interesting result is that the bound on the condition number of the scaled system is mostly the same as for the uniform case even if the mesh contains highly anisotropic elements, provided the number of anisotropic elements is relatively small. A similar result is also achieved for n=1 dimension.
Avi Berman (The Technion, Haifa)
Diagonal stability and completely positive
Dienstag, den 30.08.2011, 16.15 Uhr in MA 313 Abstract:
The talk will consist of a short survey of the theory of completely positive matrices and relate it to a newly defined concept of a common diagonal Lyapunov matrix. A necessary and sufficient condition for the existence of such a matrix will be derived. The second part of the talk is based on a recent paper with C. King and R. Shorten.