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X-WR-CALNAME:Institute of Mathematics and Informatics
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X-WR-CALDESC:Събития за Institute of Mathematics and Informatics
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DTSTART;TZID=Europe/Sofia:20230523T160000
DTEND;TZID=Europe/Sofia:20230523T173000
DTSTAMP:20260418T060650
CREATED:20230515T125006Z
LAST-MODIFIED:20230515T125139Z
UID:14317-1684857600-1684863000@math.bas.bg
SUMMARY:Семинар по Приложна математика
DESCRIPTION:NUMERICAL SOLUTION OF MULTIDIMENSIONAL SPECTRAL FRACTIONAL DIFFUSION PROBLEMS: FROM CAFFARELLI TO BURA\nЛектор: чл.-кор. Св. Маргенов (ИИКТ-БАН)\nЧас: 15:00\nДата: 23.05.2023 г.\nМясто: Зала 503 на ИМИ-БАН \nРезюме: Fractional diffusion operators appear naturally in many areas in mathematics\, physics\, ect. The most important property of the related b.v. problems is that they are nonlocal. \nLet us consider the fractional power of a self-adjoint elliptic operator introduced through its spectral decomposition. It is also self-adjoint but nonlocal. Advanced numerical methods in this area have been heavily influenced by the pioneering work in differential operator theory by Caffarelli and Silvestre\, “An Extension Problem Associated with the Fractional Laplacian”\, 2007. \nAfter discretization\, nonlocal problems lead to linear systems with dense matrices. In the multidimensional case and domains with general geometry\, the considered problems are extremely expensive from a computational point of view. Over the past decade\, several different techniques have been proposed to localize the nonlocal operator\, thereby increasing the spatial dimension of the computational domain. \nWe have developed an alternative approach. Let A be a SPD sparse matrix arising from finite element method (FEM) or finite difference method (FDM) discretization of the initial (local) problem. \nBased on the best uniform rational approximations (BURA) of degree k of zα\, 0 ≤ z ≤ 1\, a class of efficient solution methods for algebraic systems involving Aα\, 0 < α < 1\, is proposed and analysed. Robust error estimates with respect to the condition number κ(A) are derived\, showing the exponential convergence of the BURA methods with respect to the degree of rational approximation. \nAlthough the fractional power of A is a dense matrix\, the algorithm has complexity of order O(N log2N)\, where N is the number of unknowns. At this point\, we assume that some solver of optimal complexity (say multigrid or multilevel) is used for the auxiliary systems with matrices A + djI\, dj ≥ 0\, j = 1\, . . . \, k. \nThe presented (up to 3D) numerical tests are focussed on problems with low regularity of the solutions\, including cases of adaptive mesh refinement. The comparative analysis demonstrates the superiority of the BURA methods provided with rigorous theoretical results. Some recent works about BURA based preconditioning of coupled problems and non-overlapping domain decomposition methods are discussed at the end. \nФейсбук страница на семинара: Семинар по Приложна математика
URL:https://math.bas.bg/event/%d1%81%d0%b5%d0%bc%d0%b8%d0%bd%d0%b0%d1%80-%d0%bf%d0%be-%d0%bf%d1%80%d0%b8%d0%bb%d0%be%d0%b6%d0%bd%d0%b0-%d0%bc%d0%b0%d1%82%d0%b5%d0%bc%d0%b0%d1%82%d0%b8%d0%ba%d0%b0-4/
LOCATION:Институт по математика и информатика – БАН\, Block 8\, 1113 БАН IV км.\, София\, Bulgaria
CATEGORIES:Редовен семинар
ORGANIZER;CN="%D0%98%D0%BD%D1%81%D1%82%D0%B8%D1%82%D1%83%D1%82%20%D0%BF%D0%BE%20%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20%D0%B8%20%D0%B8%D0%BD%D1%84%D0%BE%D1%80%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%20-%20%D0%91%D0%90%D0%9D":MAILTO:office@math.bas.bg
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BEGIN:VEVENT
DTSTART;TZID=Europe/Sofia:20230528T090000
DTEND;TZID=Europe/Sofia:20230531T170000
DTSTAMP:20260418T060650
CREATED:20230320T093240Z
LAST-MODIFIED:20230320T094029Z
UID:14026-1685264400-1685552400@math.bas.bg
SUMMARY:SPCSC 2023: Sphere packings\, coverings\, and spherical codes
DESCRIPTION:Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences\nFaculty of Mathematics and Informatics\, Sofia University “St. Kliment Ohridski”\norganize \nInternational Workshop \n\nSphere packings\, coverings\, and spherical codes\nSPCSC 2023\n\n\nMay 28 – 31\, 2023\,\nSofia\, Bulgaria \n\nThe workshop will bring together leading experts from the fields of Sphere packings\, sphere coverings and spherical codes to present new results and developments\, open problems and new directions. \nFor more information visit SPCSC 2023 web page.
URL:https://math.bas.bg/event/international-workshop-sphere-packings-coverings-and-spherical-codes-spcsc-2023/
LOCATION:Семинар по Приложна математика
CATEGORIES:Конференция
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