The finite-element method provides a convenient and flexible procedure for the calculation of energy eigenvalues of quantum mechanical systems. The levels of accuracy that can be attained in the method of finite elements are investigated using various approximations. This is illustrated by first considering two classic examples that form a convenient basis for describing the calculational technique: the radial equation for the hydrogen atom for spherically symmetric states and the simple harmonic oscillator problem in one dimension. These two illustrative examples provide guidelines in the calculation of the energy levels of the hydrogen atom in an arbitrary spatially uniform magnetic field, a problem not solvable by analytical means. The results obtained for the Iso and 2so levels are the most accurate reported so far.This application shows that finite-element analysis can be employed with advantage for obtaining very accurate results for the energy levels and wavefunctions for quantum mechanical systems.

We continue our study of the core helium flash using the three dimensional hydrodynamics code Djehuty. Continuing from earlier calculations, we now take relaxed 3D configurations and add various amounts of rotation. We find that rotation periods consistent with those observed in white dwarfs produce negligible changes in the structure and evolution of the core flash, at least for the very small timescales we have yet been able to investigate. There is no sign of any extra mixing due to the rotation. There is some inconclusive evidence for a slight change in the luminosity, at the 1% level.

The HPC Challenge (HPCC) Benchmark suite and the Intel MPI Benchmark (IMB) are used to compare and evaluate the combined performance of processor, memory subsystem and interconnect fabric of five leading supercomputers-SGI Altix BX2, Cray X1, Cray Opteron Cluster, Dell Xeon Cluster, and NEC SX-8. These five systems use five different networks (SGI NUMALINK4, Cray network, Myrinet, InfiniBand, and NEC IXS). The complete set of HPCC Benchmarks are run on each of these systems. Additionally, we present Intel MPI Benchmarks results to study the performance of 11 MPI communication functions on these systems.

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