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UID:news-1537@dmi.unibas.ch
DTSTAMP:20231013T095041
DTSTART;TZID=Europe/Zurich:20231020T110000
DTEND;TZID=Europe/Zurich:20231020T120000
SUMMARY:Seminar in Numerical Analysis: Marco Zank (U Wien)
LOCATION:
DESCRIPTION:For the discretization of time-dependent partial differential e
quations, the standard approaches are explicit or implicit time
-stepping schemes together with finite element methods in space
. An alternative approach is the usage of space-time methods, w
here the space-time domain is discretized and the resulting glo
bal linear system is solved at once. In this talk, some recent
developments in space-time finite element methods are reviewed.
For this purpose, the heat equation and the wave equation serv
e as model problems. First, for both model problems, space-time
variational formulations and their unique solvability in space
-time Sobolev spaces are discussed, where a modified Hilbert tr
ansformation is used such that ansatz and test spaces are equal
. Second, conforming discretization schemes, using piecewise po
lynomial, globally continuous functions, are introduced. Solvab
ility and stability of these numerical schemes are discussed. N
ext, we investigate efficient direct solvers for the occurring
huge linear systems. The developed solvers are based on the Bar
tels--Stewart method and on the Fast Diagonalization method, wh
ich result in solving a sequence of spatial subproblems. The so
lver based on the Fast Diagonalization method allows solving th
ese spatial subproblems in parallel, leading to a full parallel
ization in time. In the last part of the talk, numerical exampl
es are shown and discussed.\r\n \r\nFor further information ab
out the seminar, please visit this webpage [https://dmi.unibas.
ch/de/forschung/mathematik/seminar-in-numerical-analysis/].
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