Performance of distributed multiscale simulations.

Multiscale simulations model phenomena across natural scales using monolithic or component-based code, running on local or distributed resources. In this work, we investigate the performance of distributed multiscale computing of component-based models, guided by six multiscale applications with different characteristics and from several disciplines. Three modes of distributed multiscale computing are identified: supplementing local dependencies with large-scale resources, load distribution over multiple resources, and load balancing of small- and large-scale resources.

Unstable periodic orbits in the Lorenz attractor.

We apply a new method for the determination of periodic orbits of general dynamical systems to the Lorenz equations. The accuracy of the expectation values obtained using this approach is shown to be much larger and have better convergence properties than the more traditional approach of time averaging over a generic orbit. Finally, we discuss the relevance of the present work to the computation of unstable periodic orbits of the driven Navier-Stokes equations, which can be simulated using the lattice Boltzmann method.

New variational principles for locating periodic orbits of differential equations.

We present new methods for the determination of periodic orbits of general dynamical systems. Iterative algorithms for finding solutions by these methods, for both the exact continuum case, and for approximate discrete representations suitable for numerical implementation, are discussed. Finally, we describe our approach to the computation of unstable periodic orbits of the driven Navier-Stokes equations, simulated using the lattice Boltzmann equation.

Real science at the petascale.

We describe computational science research that uses petascale resources to achieve scientific results at unprecedented scales and resolution. The applications span a wide range of domains, from investigation of fundamental problems in turbulence through computational materials science research to biomedical applications at the forefront of HIV/AIDS research and cerebrovascular haemodynamics. This work was mainly performed on the US TeraGrid 'petascale' resource, Ranger, at Texas Advanced Computing Center, in the first half of 2008 when it was the largest computing system in the world available for open scientific research.