BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Howard Elman (University of Maryland) DTSTART:20200930T140000Z DTEND:20200930T150000Z DTSTAMP:20260423T041524Z UID:E-NLA/17 DESCRIPTION:Title: M ultigrid Methods for Computing Low-Rank Solutions to Parameter-Dependent P artial Differential Equations\nby Howard Elman (University of Maryland ) as part of E-NLA - Online seminar series on numerical linear algebra\n\n \nAbstract\nThe collection of solutions of discrete parameter-dependent pa rtial differential equations often takes the form of a low-rank matrix. We show that in this scenario\, iterative algorithms for computing these sol utions can take advantage of low-rank structure to reduce both computation al effort and memory requirements. Implementation of such solvers requires that explicit rank-compression computations be done to truncate the ranks of intermediate quantities that must be computed. We prove that when trun cation strategies are used as part of a multigrid solver\, the resulting a lgorithms retain "textbook" (grid-independent) convergence rates\, and we demonstrate how the truncation criteria affect convergence behavior. In ad dition\, we show that these techniques can be used to construct efficient solution algorithms for computing the eigenvalues of parameter-dependent o perators. In this setting\, parameterized eigenvectors can be grouped into matrices of low-rank structure\, and we introduce a variant of inverse su bspace iteration for computing them. We demonstrate the utility of this a pproach on two benchmark problems\, a stochastic diffusion problem with so me poorly separated eigenvalues\, and an operator derived from a discrete Stokes problem whose minimal eigenvalue is related to the inf-sup stabilit y constant.\n\nThis is joint work with Tengfei Su.\n LOCATION:https://researchseminars.org/talk/E-NLA/17/ END:VEVENT END:VCALENDAR