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UID:submissions.pasc-conference.org_PASC23_sess184_pap122@linklings.com
SUMMARY:Exploiting Symmetries for Preconditioning Poisson's Equation in CF
D Simulations
DESCRIPTION:Paper\n\nŔdel Alsalti-Baldellou (Polytechnic University of Cat
alonia, Termo Fluids SL); Carlo Janna (University of Padova, M3E srl); Xav
ier Álvarez-Farré (SURF); and F. Xavier Trias (Polytechnic University of C
atalonia)\n\nDivergence constraints are present in the governing equations
of many physical phenomena, and they usually lead to a Poisson equation w
hose solution is one of the most challenging parts of scientific simulatio
n codes. Indeed, it is the main bottleneck of incompressible Computational
Fluid Dynamics (CFD) simulations, and developing efficient and scalable P
oisson solvers is a critical task. This work presents an enhanced variant
of the Factored Sparse Approximate Inverse (FSAI) preconditioner. It arise
s from exploiting *s* spatial reflection symmetries, which are ofte
n present in academic and industrial configurations and allow transforming
Poisson's equation into a set of 2^*s* fully-decoupled subsystems.
Then, we introduce another level of approximation by taking advantage of
the subsystems' close similarity and applying the same FSAI to all of them
. This leads to substantial memory savings and notable increases in the ar
ithmetic intensity resulting from employing the more compute-intensive spa
rse matrix-matrix product. Of course, recycling the same preconditioner on
all the subsystems worsens its convergence. However, this effect was much
smaller than expected and made us introduce relatively cheap but very eff
ective low-rank corrections. A key feature of these corrections is that th
anks to being applied to each subsystem independently, the more symmetries
being exploited, the more effective they become, leading to up to 5.7x fa
ster convergences than the standard FSAI. Numerical experiments on up to 1
.07 billion grids confirm the quality of our low-rank corrected FSAI, whic
h, despite being 2.6x lighter, outperforms the standard FSAI by a factor o
f up to 4.4x.\n\nDomain: Engineering, Computer Science, Machine Learning,
and Applied Mathematics
\n\nSession Chair: Nur Aiman Fadel (ETH Zurich /
CSCS)
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