BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news1537@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20231013T095041 DTSTART;TZID=Europe/Zurich:20231020T110000 SUMMARY:Seminar in Numerical Analysis: Marco Zank (U Wien) 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 appr oach is the usage of space-time methods\, where the space-time domain is d iscretized and the resulting global linear system is solved at once. In th is talk\, some recent developments in space-time finite element methods ar e reviewed. For this purpose\, the heat equation and the wave equation ser ve as model problems. First\, for both model problems\, space-time variati onal formulations and their unique solvability in space-time Sobolev space s are discussed\, where a modified Hilbert transformation is used such tha t ansatz and test spaces are equal. Second\, conforming discretization sch emes\, using piecewise polynomial\, globally continuous functions\, are in troduced. Solvability and stability of these numerical schemes are discuss ed. Next\, we investigate efficient direct solvers for the occurring huge linear systems. The developed solvers are based on the Bartels--Stewart me thod and on the Fast Diagonalization method\, which result in solving a se quence of spatial subproblems. The solver based on the Fast Diagonalizatio n method allows solving these spatial subproblems in parallel\, leading to a full parallelization in time. In the last part of the talk\, numerical examples are shown and discussed.\\r\\n\\r\\nFor further information about the seminar\, please visit this webpage [t3://page?uid=1115]. X-ALT-DESC:

For the discretization of time-dependent partial differential equations\, the standard approaches are explicit or implicit time-steppin g schemes together with finite element methods in space. An alternative ap proach is the usage of space-time methods\, where the space-time domain is discretized and the resulting global 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 s erve as model problems. First\, for both model problems\, space-time varia tional formulations and their unique solvability in space-time Sobolev spa ces are discussed\, where a modified Hilbert transformation is used such t hat ansatz and test spaces are equal. Second\, conforming discretization s chemes\, using piecewise polynomial\, globally continuous functions\, are introduced. Solvability and stability of these numerical schemes are discu ssed. Next\, we investigate efficient direct solvers for the occurring hug e linear systems. The developed solvers are based on the Bartels--Stewart method and on the Fast Diagonalization method\, which result in solving a sequence of spatial subproblems. The solver based on the Fast Diagonalizat ion method allows solving these spatial subproblems in parallel\, leading to a full parallelization in time. In the last part of the talk\, numerica l examples are shown and discussed.

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For further information abou t the seminar\, please visit this webpage.

DTEND;TZID=Europe/Zurich:20231020T120000 END:VEVENT END:VCALENDAR