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:news1455@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20230403T123724 DTSTART;TZID=Europe/Zurich:20230414T110000 SUMMARY:Seminar in Numerical Analysis: Vesa Kaarnioja (FU Berlin) DESCRIPTION:We describe a fast method for solving elliptic PDEs with uncert ain coefficients using kernel-based interpolation over a rank-1 lattice po int set [1]. By representing the input random field of the system using a model proposed by Kaarnioja\, Kuo\, and Sloan [2]\, in which a countable n umber of independent random variables enter the random field as periodic f unctions\, it is shown that the kernel interpolant can be constructed for the PDE solution (or some quantity of interest thereof) as a function of t he stochastic variables in a highly efficient manner using fast Fourier tr ansform. The method works well even when the stochastic dimension of the p roblem is large\, and we obtain rigorous error bounds which are independen t of the stochastic dimension of the problem. We also outline some techniq ues that can be used to further improve the approximation error and comput ational complexity of the method [3].\\r\\n\\r\\nReferences:\\r\\n[1] V. K aarnioja\, Y. Kazashi\, F. Y. Kuo\, F. Nobile\, and I. H. Sloan. Fast appr oximation by periodic kernel-based lattice-point interpolation with applic ation in uncertainty quantification. Numer. Math. 150:33-77\, 2022.\\r\\n[ 2] V. Kaarnioja\, F. Y. Kuo\, and I. H. Sloan. Uncertainty quantification using periodic random variables. SIAM J. Numer. Anal. 58(2):1068-1091\, 20 20.\\r\\n[3] V. Kaarnioja\, F. Y. Kuo\, and I. H. Sloan. Lattice-based ker nel approximation and serendipitous weights for parametric PDEs in very hi gh dimensions. Preprint 2023\, arXiv:2303.17755 [math.NA].\\r\\n\\r\\nFor further information about the seminar\, please visit this webpage [t3://pa ge?uid=1115]. X-ALT-DESC:

We describe a fast method for solving elliptic PDEs with unce rtain coefficients using kernel-based interpolation over a rank-1 lattice point set [1]. By representing the input random field of the system using a model proposed by Kaarnioja\, Kuo\, and Sloan [2]\, in which a countable number of independent random variables enter the random field as periodic functions\, it is shown that the kernel interpolant can be constructed fo r the PDE solution (or some quantity of interest thereof) as a function of the stochastic variables in a highly efficient manner using fast Fourier transform. The method works well even when the stochastic dimension of the problem is large\, and we obtain rigorous error bounds which are independ ent of the stochastic dimension of the problem. We also outline some techn iques that can be used to further improve the approximation error and comp utational complexity of the method [3].

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References:

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[1] V. Kaarnioja\, Y. Kazashi\, F. Y. Kuo\, F. Nobile\, and I. H. Sloan. Fast approximation by periodic kernel-based lattice-point interpolation with ap plication in uncertainty quantification. Numer. Math. 150:33-77\, 2022.

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[2] V. Kaarnioja\, F. Y. Kuo\, and I. H. Sloan. Uncertainty quantifi cation using periodic random variables. SIAM J. Numer. Anal. 58(2):1068-10 91\, 2020.

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[3] V. Kaarnioja\, F. Y. Kuo\, and I. H. Sloan. Lattice -based kernel approximation and serendipitous weights for parametric PDEs in very high dimensions. Preprint 2023\, arXiv:2303.17755 [math.NA].

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For further information about the seminar\, please visit this webpag e.

DTEND;TZID=Europe/Zurich:20230414T120000 END:VEVENT END:VCALENDAR