[Crib-list] Reminder... VIRTUAL "CRIBB Seminar" -- Spk. Mohammad Shafaet Islam (MIT) - Friday, March 3, 2023

[Shirley Entzminger]

VIRTUAL...

         COMPUTATIONAL RESEARCH in BOSTON and BEYOND SEMINAR
    (CRIBB)


   ZOOM meeting info...

https://mit.zoom.us/j/96155042770

Meeting ID: 961 5504 2770

====================================

DATE:	Friday, March 3, 2023

TIME:	12:00 PM - 1:00 PM


SPEAKER:  Mohammad Shafaet Islam  (MIT)


TITLE:	Accelerating the Jacobi Iteration for Solving Linear Systems of
  Equations using Theory, Data and High Performance Computing


ABSTRACT:

High fidelity scientific 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 solution of these linear systems often takes a vast amount 
of
computational time to compute. Solving these linear systems efficiently 
requires
the use of massively 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
performance.

This talk offers two key components towards the development of a memory
efficient linear solver algorithm tailored towards high performance 
computing
(HPC) systems. Firstly, starting with the Jacobi iteration (a parallel 
linear
solver algorithm well-suited for HPC), we develop a family of relaxation 
schemes
which greatly improve the convergence of the method. These schemes, 
termed
Scheduled Relaxation Jacobi (SRJ) schemes, provide acceleration for both
symmetric and nonsymmetric linear systems of equations. In the symmetric 
case, a
data informed heuristic is developed to aid scheme selection in a 
practical
implementation without user intervention. Secondly, we develop a
high-performance GPU implementation of the Jacobi iteration method. The 
main
characteristic of the linear solver is that it utilizes 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 grids. The shared memory Jacobi 
linear
solver demonstrates improved performance over a classical GPU 
implementation
which relies solely on global memory for solving two-dimensional 
unstructured
problems. These contributions provide the basis for an efficient GPU 
linear
solver for the solution of (potentially unstructured/nonsymmetric) 
linear
systems arising from simulation.

=======================================

For information about the "Computational Research in Boston and Beyond 
Seminar"
(CRIBB), please visit:

https://math.mit.edu/sites/crib/


=================

Shirley A. Entzminger
Administrative Assistant II
Department of Mathematics
Massachusetts Institute of Technology
77 Massachusetts Avenue
Building 2, Room 350A
Cambridge, MA 02139
PHONE: 	(617) 253-4994
E-mail:	daisymae at math.mit.edu
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