Simulating Quarks and Gluons with

Quantum Chromodynamics

February 10, 2005. CS635 Parallel Computer Architecture. Mahantesh Halappanavar.

Impact on Science

LQCD will impact science at all scales. Major Goals:

Verify the standard model (discover the limits) Determine properties of interacting matter

under extreme conditions Understand internal structure of nucleons and

other strongly interacting particles. Lattice QCD simulations are essential to

research in all of these areas. Possible only by computation, results needed

urgently to support the experimental work (like Relativistic Heavy Ion Collider - BNL)

Scientific Opportunities

With sustained computational power of 100 Tflops/s (currently ~1Tflops) and improved lattice formulations, major advances in our understanding of internal structure of nucleons can be made.

Pflops/s resources would enable study of the gluon structure of the nucleon, in addition to its quark structure.

These calculations would significantly deepen our understanding of the standard model and therefore of the basic laws of physics.

Research Issues

QCD is formulated in the four-dimensional space-time continuum and involves hundreds of millions of variables.

Simulations need to be done at small distances which grows at approximately as the seventh power of the inverse of the lattice spacing.

Up and down quarks have very small mass and therefore cannot be represented accurately (need Pflop/s computational power).

Dirac operator: 70-90% of computations – sparse matrix & iterative techniques. Standard multilevel solver techniques to accelerate inversion cannot be used due to random nature of the nonzero elements of the Dirac operator.

New algorithms needed for QCD at large densities and time dependent problems.

Resources Required:

Need for special type of machines: Commercial cache based machine: 10-15% Specially designed: 35-50%

Basic operation: multiplication of a three component vector of complex numbers, by a 3 X 3 matrix of complex numbers.

Critical: relationship between data movement and floating point operations. Regular architectures would prove to be insufficient.

Special machines at FNAL and JLab.

“More Science Per Dollar”

First production three-dimensional mesh computer system in the world.

Prototype 256-node 3-D Gigabit Ethernet mesh Linux cluster arranged in 4X8X8 (torus) configuration using Intel PRO/1000 MT Dual Port Server Adapters as the interconnect.

Intel Xeon processor based node is wired point-to-point to six adjacent nodes using three Intel Cards, eliminating need for a switch.

~0.7 teraflops sustained, data rates approaching 500 MB/sec/node have been achieved.

Metrics of Success

True success will be generation of new results with accuracies sufficient to advance current understanding of fundamental theory.

Make precise tests on Standard Model and develop more encompassing theory than the Standard Model.

All this is possible when the required computational resources will become available.

THANKS !!