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DTSTART;TZID=Europe/Stockholm:20190613T171500
DTEND;TZID=Europe/Stockholm:20190613T174500
UID:submissions.pasc-conference.org_PASC19_sess140_msa252@linklings.com
SUMMARY:MFEM: Accelerating Efficient Solution of PDEs at Exascale
DESCRIPTION:Minisymposium\nComputer Science and Applied Mathematics, Engin
eering\n\nMFEM: Accelerating Efficient Solution of PDEs at Exascale\n\nKol
ev\n\nEfficient exploitation of exascale architectures requires rethinking
of the numerical algorithms used in large-scale PDE-based applications. T
hese architectures will favor algorithms, such as high-order finite elemen
ts, that expose fine-grain parallelism and maximize the ratio of floating
point operations to energy intensive data movement. In this talk we presen
t an overview of MFEM (mfem.org), a scalable library for high-order finite
element discretization of PDEs on general unstructured grids. We also rep
ort on recent work in the Center for Efficient Exascale Discretizations (h
ttp://ceed.exascaleproject.org), a co-design center in the US Exascale Com
puting Project focused on next-generation discretization software and algo
rithms. Our approach to efficiency is based on a "matrix-free" representat
ion of the finite element operator, that factors a bilinear form into a se
ries of sparse and dense components corresponding to the parallelism, mesh
topology, basis, geometry, and pointwise physics in the problem. The oper
ator decomposition exposes several layers of parallelism, enables the use
of batched dgemms and tensor contractions, and only requires quadrature po
int values to be assembled for computing the action. This "partial assembl
y" formulation results both in less (nearly optimal) computation and less
(optimal) data movement compared to assembling a global sparse matrix, the
refore increasing performance and reducing time to solution.
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