in
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Norfolk
Marriott Waterside
Exhibits Chair
in
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HighPerformance Computing Symposium 2007 (HPC'07)Plenary Keynote Speakerspart of the

Mathematical Software for Highend Computational Science and EngineeringDavid E. KeyesFu Foundation Professor of Applied Mathematics Department of Applied Physics and Applied Mathematics Columbia University New York City, New York 
Multiscale, multirate scientific and engineering applications based
on systems of partial differential equations possess resolution
requirements that are typically inexhaustible and demand execution on
the highestcapability computers available, which will soon reach the
petascale. While the variety of applications is enormous, their needs
for mathematical software infrastructure are surprisingly coincident.
Domains with complex geometry require versatile meshing and
discretization tools. Resolution requirements that evolve with the
solution require dynamic adaptivity. Implicit methods for stable and
accurate integration of transient problems and efficient treatments for
equilibrium problems lead to large, illconditioned algebraic systems
that must be solved with an algorithmic complexity that is close to
linear in problem size or storage complexity. Distributed memory
architectures demand efficient means of creating and managing
loadbalanced partitions of unstructured objects. These and other
algorithmic challenges that are generic to nearly all mesh and
particlebased applications are addressed in the SciDAC Institute and
Centers for Enabling Technologies in mathematics, which we briefly
overview in this talk. The chief bottleneck to scalability is often the solver. At their current scalability limits, many applications spend a vast majority of their operations in solvers, due to solver algorithmic complexity that is superlinear in the problem size, whereas other phases scale linearly. Furthermore, the solver may be the phase of the simulation with the poorest parallel scalability, due to intrinsic global dependencies. The Towards Optimal PDE Simulations (TOPS) center focuses on relieving this bottleneck while providing a multilevel programming interface that allows users to advance from initial concerns of correctness and robustness to ultimate concerns of efficiency and performance portability. 
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