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SUMMARY:CCM Seminar: Yang Liu (LBNL)
DTSTART;VALUE=DATE-TIME:20210512T140000Z
DTEND;VALUE=DATE-TIME:20210512T151500Z
DTSTAMP;VALUE=DATE-TIME:20210926T162900Z
UID:indico-event-1967@indico.flatironinstitute.org
DESCRIPTION:"Fast\, Direct Integral and Differential Equation Solvers for
Electromagnetic\, Acoustic\, and Elastic Applications at All Frequency Ran
ges"\n\nAbstract: Large-scale and full-wave modeling for acoustic and ela
stic inversion applications\, analysis and synthesis of electromagnetic sy
stems for traditional and emerging RF\, microwave\, terahertz applications
rely on efficient numerical tools. Integral equation (i.e.\, method of mo
ment) and differential equation (e.g.\, finite-difference\, finite-element
\, and finite-volume) formulations lead to dense and sparse linear systems
\, respectively. These linear systems can be solved by either iterative or
direct solvers. Iterative solvers\, despite their success in constructing
well-conditioned formulations and fast multipole-type algorithms\, remain
inefficient for systems that are inherently ill-conditioned and/or requir
e multiple right-hand sides. This is particularly true for design automati
on\, inverse scattering\, and other coupled systems where iterative solver
s often require forbiddingly high iteration time. Direct solvers\, in star
k contrast\, can attain reliable solutions in a predictable time. However\
, exact direct solvers typically require O(N3) and O(N2) computational cos
ts for dense and sparse systems of size N\, respectively. Fast direct solv
ers\, on the other hand\, rely on the fact that off-diagonal blocks of the
well-ordered linear systems can be compressed by numerical linear algebra
tools including low-rank and butterfly decompositions. When further embed
ded in hierarchical matrix frameworks\, such as H-matrix\, hierarchically
off-diagonal low-rank (HODLR)\, and hierarchically semi-separable (HSS) fo
rmats\, these direct solvers and preconditioners can achieve quasi-linear
complexities for construction\, factorization and solution for the discret
ized systems across all frequency ranges. We will review the development o
f these solvers in the past two decades\, with an emphasis on their butter
fly-based variants and distributed-memory parallelization for high-frequen
cy problems. An open source package integrating most techniques reviewed\,
called ButterflyPACK\, will also be introduced.\n\nSee: https://crd.lbl.g
ov/departments/applied-mathematics/scalable-solvers/members/staff-members/
yang-liu/\nhttps://indico.flatironinstitute.org/event/1967/
URL:https://indico.flatironinstitute.org/event/1967/
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