KAUST's David Keyes takes graphics
cards beyond gaming
January 16, 2017
graphics cards found in powerful gaming computers are now capable of
solving computationally intensive mathematical problems common in
science and engineering applications, thanks to a new solver developed
by researchers from the KAUST Extreme Computing Research Center.
"One of the most common problems in scientific and engineering computing
is solving systems of multiple simultaneous equations involving
thousands to millions of variables," said David Keyes, KAUST Professor
of Applied Mathematics and Computational Science, who also led the
research team. "This type of problem comes up in statistics,
optimization, electrostatics, chemistry, mechanics of solid bodies on
Earth and gravitational interactions among celestial bodies in space."
In typical applications, solving such problems is often the main
computational cost. Thus, acceleration of the solver has the potential
to considerably impact both the execution time and the energy
consumption required to solve the problem.
"Graphics processing units (GPUs) are very energy efficient compared
with standard high-performance processors because they eliminate a lot
of the hardware required for standard processors to execute
general-purpose code," explained Keyes. "However, GPUs are new enough
that their supporting software remains immature. With the expertise of
Ali Charara, a Ph.D. student in the Center who spent several months as
an intern at NVIDIA in California, we have been able to identify many
things that we can either innovate or improve upon, such as redesigning
a common solver."
key to making a more efficient solver is maximizing the trade-off
between the number of processors and the memory available to temporarily
store the computational data. Memory remains expensive, so finding a way
to execute more computation using less memory is critical to solving the
problem of computational cost.
"Charara designed a solver scheme that operates directly on data 'in
place' without making an extra copy," explained Hatem Ltaief, a Senior
Research Scientist from the project's team. "This means a system twice
as large can be stored in the same amount of memory."
Charara achieved this by converting operations that are often carried
out by progressing sequentially over columns in the data into a series
of tasks on small, computationally efficient, rectangular and triangular
blocks recursively carved out of the matrix. This performed specifically
on columns in the matrix of values derived from the set of simultaneous
equations. This redesigned triangular matrix-matrix multiplication
implementation achieves up to eightfold acceleration compared to that of
"Now, every user of an NVIDIA GPU has a faster solver for a common task
in scientific and engineering computing at their disposal," said Keyes.
The solver is due to be integrated into the next scientific software
library for NVIDIA GPUs.