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X-WR-CALDESC:Събития за Institute of Mathematics and Informatics
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DTSTART:20250330T010000
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DTSTART;TZID=Europe/Sofia:20250724T140000
DTEND;TZID=Europe/Sofia:20250724T153000
DTSTAMP:20260418T231826
CREATED:20250717T081421Z
LAST-MODIFIED:20250717T081421Z
UID:18024-1753365600-1753371000@math.bas.bg
SUMMARY:Семинар "Математически основи на информатиката"
DESCRIPTION:Следващата сбирка на семинара на секция \nМАТЕМАТИЧЕСКИ ОСНОВИ НА ИНФОРМАТИКАТА \nще се състои в сряда\, 24.07.2025\, от 14:00 часа\, в зала 403 на ИМИ\, на която \nпроф. Марк Айуън\nще изнесе доклад на тема: \nSparse Spectral Methods for Solving High-Dimensional and Multiscale Elliptic PDEs\nПроф. Айуън работи в департамента по изчислителна математика в Michigan State University и има широки интереси свързани с обработката на данни и обработката на сигнали. Темата\, която предложи за семинара има някои неочаквани връзки с определени шумозащитни кодове.\nРезюме. In his monograph “Chebyshev and Fourier Spectral Methods”\, John Boyd claimed that\, regarding Fourier spectral methods for solving differential equations\, “[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless march to larger and larger [bandwidths] continues” [1\, pg. 194]. This talk will discuss attempts to further the virtue of the Fast Fourier Transform (FFT) as not only bandwidth is pushed to its limits\, but also the dimension of the problem. Instead of using the traditional FFT however\, we make a key substitution from the sublinear-time compressive sensing literature: a high-dimensional\, sparse Fourier transform (SFT) paired with randomized rank-1 lattice methods. The resulting sparse spectral method rapidly and automatically determines a set of Fourier basis functions whose span is guaranteed to contain an accurate approximation of the solution of a given elliptic PDE. This much smaller\, near-optimal Fourier basis is then used to efficiently solve the given PDE in a runtime which only depends on the PDE’s data/solution compressibility and ellipticity properties\, while breaking the curse of dimensionality and relieving linear dependence on any multiscale structure in the original problem. Theoretical performance of the method is established with convergence analysis in the Sobolev norm for a general class of nonconstant diffusion equations\, as well as pointers to technical extensions of the convergence analysis to more general advection-diffusion-reaction equations. Numerical experiments demonstrate good empirical performance on several multiscale and high-dimensional example problems\, further showcasing the promise of the proposed methods in practice.
URL:https://math.bas.bg/event/%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d1%87%d0%b5%d1%81%d0%ba%d0%b8-%d0%be%d1%81%d0%bd%d0%be%d0%b2%d0%b8-%d0%bd%d0%b0-%d0%b8%d0%bd%d1%84%d0%be-6/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
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