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CATEGORIES:Conferences/Seminars/Lectures
DESCRIPTION:Speaker: Mohammad Shafaet Islan (MIT)\n\nTitle: Accelerating
the Jacobi Iteration for Solving Linear Systems of Equations using Theory\
, Data and High Performance Computing\n\nAbstract:\n\nHigh fidelity scienti
fic simulations modeling physical phenomena typically require solving large
sparse linear systems of equations which result from the discretization of
a partial differential equation (PDE) by some numerical method. The soluti
on of these linear systems often takes a vast amount of computational time
to compute. Solving these linear systems efficiently requires the use of ma
ssively parallel hardware with high computational throughput (such as GPUs)
\, as well as the development of linear solver algorithms which respect the
memory hierarchy of these hardware architectures to achieve the best perfo
rmance.\n\n\nThis talk offers two key components towards the development of
a memory efficient linear solver algorithm tailored towards high performan
ce computing (HPC) systems. Firstly\, starting with the Jacobi iteration (a
parallel linear solver algorithm well-suited for HPC)\, we develop a famil
y of relaxation schemes which greatly improve the convergence of the method
. These schemes\, termed Scheduled Relaxation Jacobi (SRJ) schemes\, provid
e acceleration for both symmetric and nonsymmetric linear systems of equati
ons. In the symmetric case\, a data informed heuristic is developed to aid
scheme selection in a practical implementation without user intervention. S
econdly\, we develop a high-performance GPU implementation of the Jacobi it
eration method. The main characteristic of the linear solver is that it uti
lizes on-chip shared memory for improved memory efficiency. This is enabled
by the unstructured swept rule\, an algorithm for space-time decomposition
which enables efficient stencil computations in parallel on unstructured g
rids. The shared memory Jacobi linear solver demonstrates improved performa
nce over a classical GPU implementation which relies solely on global memor
y for solving two-dimensional unstructured problems. These contributions pr
ovide the basis for an efficient GPU linear solver for the solution of (pot
entially unstructured/nonsymmetric) linear systems arising from simulation.
\n\n \n\n \n\nhttps://mit.
zoom.us/j/96155042770
DTEND:20230303T180000Z
DTSTAMP:20241109T141328Z
DTSTART:20230303T170000Z
LOCATION:
SEQUENCE:0
SUMMARY:Computational Research in Boston and Beyond Seminar (CRIBB)
UID:tag:localist.com\,2008:EventInstance_42527121328040
URL:https://calendar.mit.edu/event/computational_research_in_boston_and_bey
ond_seminar_9062
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