November/December 2006 News Notes from the LLNL Institute for Scientific Computing Research (ISCR)

Breakthroughs that are ultimately delivered to applications groups at the Laboratory in the form of general-purpose software are often initiated or catalyzed by academic visitors to the ISCR. For example, LLNL's Hypre scalable solver library now includes the first provably scalable solver for the positive semi-definite form of Maxwell's equations on general unstructured meshes, which is directly traceable to a March 2006 seminar by computational mathematician Jinchao Xu of PennState. Hypre is one of the mainstays of NNSA's ASC program and of the Office of Science's SciDAC program. As the number of processors in a tightly coupled parallel computer now exceeds 100,000 and the number of discrete elements in a three-dimensional mesh-based or particle-based code now routinely exceeds one billion, traditional solvers may still fit into memory, but their convergence degrades so that the additional resolution afforded to a multiscale is not practically useful. Hypre's multilevel solvers maintain their convergence as the mesh is refined for many problems, but Maxwell problems (which describe electromagnetic fields and arise in many Laboratory missions) have defied both theory and robust practice on general unstructured meshes until now. ISCR visitor Xu showed how to reduce a typical Maxwell problem to a series of problems that Hypre is already equipped to solve optimally. ISCR post-doc Tzanio Kolev and CASC senior scientist Panayot Vassilevski have published several 2006 reports and papers further developing the technique and demonstrating its value. (Keyes, 2-1325)