Impact of ORNL Mathematics and Algorithm Development Activities on Grand Challenge Applications

In developing computational models of physical processes, researchers have to deal with large systems of complex equations. Just getting the proper physics is a daunting task. Getting the computer code representing those equations to run efficiently, and on computer systems with limited memory or with I/O bottlenecks, is an added challenge. ORNL researchers have addressed that challenge by developing and distributing algorithms and numerical methods that are portable, scalable, and efficient:

• Eigenvalue methods
• QMRPACK (Quasi-Minimal Residual)
• Dolib and Donio (saving memory and I/O)
• BLAS (Basic Linear Algebra Subprograms)
• Sparse direct solvers
• Dense matrix solvers (lapack and Scalapack)
• Distributed computing environments (PVM, XPVM, MPI)
• K-space wavelets