
Title: Solution of a ThreeBody Problem in Quantum Mechanics Using Sparse Linear Algebra on Parallel Computers

Authors:
Mark Baertschy (University of Colorado)
Xiaoye Li (Lawrence Berkeley National Laboratory)

Abstract:
A complete description of two outgoing electrons following an ionizing collision between a single electron and an atom or molecule has long stood as one of the unsolved fundamental problems in quantum collision theory. In this paper we describe our use of distributed memory parallel computers to calculate a fully converged wave function describing the electronimpact ionization of hydrogen. Our approach hinges on a transformation of the Schrodinger equation that simplifies the boundary conditions but requires solving very illconditioned systems of a few million complex, sparse linear equations. We developed a twolevel iterative algorithm that requires repeated solution of sets of a few hundred thousand linear equations. These are solved directly by LU factorization using a specially tuned, distributed memory parallel version of the sparse LU factorization library SuperLU. In smaller cases, where direct solution is technically possible, our iterative algorithm still gives significant savings in time and memory despite lower megaflop rates.

Title: Parallel implementation and performance of fastDNAml  a program for maximum likelihood phylogenetic inference

Authors:
Craig A. Stewart (Indiana University)
David Hart (Indiana University)
Donald K. Berry (Indiana University)
Gary J. Olsen (University of Illinois Urbana Champaign)
Eric A. Wernert (Indiana University)
William Fischer (Indiana University)

Abstract:
This paper describes the parallel implementation of fastDNAml, a program for the maximum likelihood inference of phylogenetic trees from DNA sequence data. Mathematical means of inferring phylogenetic trees have been made possible by the wealth of DNA data now available. Maximum likelihood analysis of phylogenetic trees is extremely computationally intensive. Availability of computer resources is a key factor limiting use of such analyses. fastDNAml is implemented in serial, PVM, and MPI versions, and may be modified to use other message passing libraries in the future. We have developed a viewer for comparing phylogenies. We tested the scaling behavior of fastDNAml on an IBM RS/6000 SP up to 64 processors. The parallel version of fastDNAml is one of very few computational phylogenetics codes that scale well. fastDNAml is available for download as source code or compiled for Linux or AIX.

Title: Modeling of Seismic Wave Propagation at the Scale of the Earth on a Large Beowulf

Authors:
Dimitri Komatitsch (California Institute of Technology)
Jeroen Tromp (California Institute of Technology)

Abstract:
We use a parallel spectralelement method to simulate the propagation of seismic waves generated by earthquakes in the entire 3D Earth. The method is implemented using MPI on a large PC cluster (Beowulf) with 151 processors and 76 Gb of RAM. It is based upon a weak formulation of the equations of motion and combines the flexibility of a finiteelement method with the accuracy of a pseudospectral method. The finiteelement mesh honors all discontinuities in the Earth velocity model. To maintain a relatively constant number of grid points per seismic wavelength, the size of the elements is increased with depth in a conforming fashion, thus retaining a diagonal mass matrix. The effects of attenuation and anisotropy are incorporated. We benchmark spectralelement synthetic seismograms against a normalmode reference solution for a spherically symmetric Earth velocity model. The two methods are in excellent agreement for all waves with periods greater than 20 seconds.