High energy electron impact ionisation of H91s in coplanar asymmetric geometry
Australian Journal of Physics
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
Analysis and comparison of two general sparse solvers for distributed memory computers
ACM Transactions on Mathematical Software (TOMS)
Making sparse Gaussian elimination scalable by static pivoting
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
SuperLU Users'' Guide
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
An overview of SuperLU: Algorithms, implementation, and user interface
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Service Oriented Approach to High Performance Scientific Computing
CCGRID '10 Proceedings of the 2010 10th IEEE/ACM International Conference on Cluster, Cloud and Grid Computing
A comparative study of iterative solutions to linear systems arising in quantum mechanics
Journal of Computational Physics
The BiCOR and CORS Iterative Algorithms for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
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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 electron-impact ionization of hydrogen. Our approach hinges on a transformation of the Schrödinger equation that simplifies the boundary conditions but requires solving very ill-conditioned systems of a few million complex, sparse linear equations. We developed a two-level 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.