Stephen T. Barnard

Fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems

SUMMARY If problems involving unstructured meshes are to be solved efficiently on distributed-memory parallel computers, the meshes must be partitioned and distributed across processors in a way that balances the computational load and minimizes communication. The recursive spectral bisection method (RSB) has been shown to be very effective for such partitioning problems compared to alternative methods, but RSB in its simplest form is expensive. Here a multilevel version of RSB is introduced that attains about an order-of-magnitude improvement in run time on typical examples. 1. INTRODUCTION Unstructured meshes are used in several large-scale scientific and engineering problems, including finite-volume methods for computational fluid dynamics and finite-element methods for structural analysis. If unstructured problems such as these are to be solved on distributed-memory parallel computers, their data structures must be partitioned and distributed across processors; if they are to be solved efficiently, the partitioning must niaximize load balance and minimize interprocessor communication. Recently, the recursive spectral bisection method (RSB)[l] has been shown to be very effective for such partitioning problems compared to alternative methods. Unfortunately, RSB in its simplest form is expensive. We shall describe a multilevel version of RSB that attains about im order-of-magnitude improvement in run time on typical examples.

Towards a fast implementation of spectral nested dissection

The authors describe the novel spectral nested dissection (SND) algorithm, a novel algorithm for computing orderings appropriate for parallel factorization of sparse, symmetric matrices. The algorithm makes use of spectral properties of the Laplacian matrix associated with the given matrix to compute separators. The authors evaluate the quality of the spectral orderings with respect to several measures: fill, elimination tree height, height and weight balances of elimination trees, and clique tree heights. They use some very large structural analysis problems as test cases and demonstrate on these real applications that spectral orderings compare quite favorably with commonly used orderings, outperforming them by a wide margin for some of these measures. The only disadvantage of SND is its relatively long execution time.<<ETX>>

An MPI Implementation of the SPAI Preconditioner on the T3E

The authors describe and test spai_1.1, a parallel MPI implementation of the sparse approximate inverse (SPAI) preconditioner. They show that SPAI can be very effective for solving a set of very large and difficult problems on a Cray T3E. The results clearly show the value of SPAI (and approximate inverse methods in general) as the viable alternative to ILU-type methods when facing very large and difficult problems. The authors strengthen this conclusion by showing that spai_1.1 also has very good scaling behavior.

A spectral algorithm for envelope reduction of sparse matrices

An algorithm for reducing the envelope of a sparse matrix is presented. This algorithm is based on the computation of eigenvectors of the Laplacian matrix associated with the graph of the sparse matrix. A reordering of the sparse matrix is determined based on the numerical values of the entries of an eigenvector of the Laplacian matrix. Numerical results show that the new reordering algorithm can in some cases reduce the envelope by more than a factor of two over the current standard algorithms such as Gibbs-Poole-Stockmeyer or SPARSPAKs reverse Cuthill-McKee.

Molecular Dynamics Simulation of Large-Scale Carbon Nanotubes on a Shared-Memory Architecture

Classical molecular dynamics simulations employing Brenners reactive potential with long range van der Waals interactions have been used in mechanistic response studies of carbon nanotubes to external strains. Elastomechanic response behavior of single and multiwall carbon nanotubes to externally applied compressive strains is simulated and studied in detail. Due to inclusion of non-bonded long range interactions, the simulations show the redistribution of strain and strain energy from sideways buckling to the formation of highly localized strained kink sites. We describe the results and discuss their implication towards the stability of any molecular mechanical structure made of carbon nanotubes.

Carbon-nanotube-based nanotechnology in an integrated modeling and simulation environment

Publisher Summary This chapter defines the requirements of a TCAD-based environment in which the basic concepts behind nanotechnology can be investigated. This involves developing physical models of nanoscale objects and conducting large-scale simulations to test the validity of these models under realistic physical and chemical conditions. The nanoscale objects then can be investigated for structural, mechanical, electronic, and transport behavior, and their integration into larger systems can be studied. The design and simulation of realistic nanotechnology systems presents formidable computational challenges. Future nanotechnology systems simulation may need to be performed for 100 million atoms. The most accurate methods available may remain limited in scope to smaller molecular systems. The application simulations have been divided into four categories: mechanical andmaterials properties of nanotubes; nanotube heterojunctions as molecular electronic device components; nanoscale electromechanical systems and a laser-driven molecular motor; and nanotube-based nanolithography on silicon surfaces. The applications of nanostructured materials and device components are just starting to be conceived and simulated.