Final Report- "An Algorithmic and Software Framework for Applied Partial Differential Equations (APDEC): A DOE SciDAC Integrated Software Infrastructure Center (ISIC)

All of the work conducted under the auspices of DE-FC02-01ER25473 was characterized by exceptionally close collaboration with researchers at the Lawrence Berkeley National Laboratory (LBNL). This included having one of my graduate students - Sarah Williams - spend the summer working with Dr. Ann Almgren a staff scientist in the Center for Computational Sciences and Engineering (CCSE) which is a part of the National Energy Research Supercomputer Center (NERSC) at LBNL. As a result of this visit Sarah decided to work on a problem suggested by Dr. John Bell the head of CCSE for her PhD thesis, which she finished in June 2007. Writing a PhD thesis while working at one of the University of California (UC) managed DOE laboratories is a long established tradition at the University of California and I have always encouraged my students to consider doing this. For example, in 2000 one of my graduate students - Matthew Williams - finished his PhD thesis while working with Dr. Douglas Kothe at the Los Alamos National Laboratory (LANL). Matt is now a staff scientist in the Diagnostic Applications Group in the Applied Physics Division at LANL. Another one of my graduate students - Christopher Algieri - who was partially supported with funds from DE-FC02-01ER25473 wrote am MS Thesis that analyzed and extended work published by Dr. Phil Colella and his colleagues in 1998. Dr. Colella is the head of the Applied Numerical Algorithms Group (ANAG) in the National Energy Research Supercomputer Center at LBNL and is the lead PI for the APDEC ISIC which was comprised of several National Laboratory research groups and at least five University PI's at five different universities. Chris Algieri is now employed as a staff member in Dr. Bill Collins' research group at LBNL developing computational models for climate change research. Bill Collins was recently hired at LBNL to start and be the Head of the Climate Science Department in the Earth Sciences Division at LBNL. Prior to this he had been a Deputy Section Head at the National Center for Atmospheric Research in Colorado. My understanding is that Chris Algieri is the first person that Bill hired after coming to LBNL. The plan is that Chris Algieri will finish his PhD thesis while employed as a staff scientist in Bill's group. Both Sarah and Chris were supported in part with funds from DE-FC02-01ER25473. In Sarah's case she received support both while at U.C. Davis (UCD) taking classes and writing an MS thesis and during some of the time she was living in Berkeley, working at LBNL and finishing her PhD thesis. In Chris' case he was at U.C. Davis during the entire time he received support from DE-FC02-01ER25473. More specific details of their work are included in the report below. Finally my own research conducted under the auspices of DE-FC02-01ER25473 either involved direct collaboration with researchers at LBNL - Phil Colella and Peter Schwartz who is a member of Phil's Applied Numerical Algorithms Group - or was on problems that are closely related to research that has been and continues to be conducted by researchers at LBNL. Specific details of this work can be found below. Finally, I would like to note that the work conducted by my students and me under the auspices of this contract is closely related to work that I have performed with funding from my DOE MICS contract DE-FC02-03ER25579 'Development of High-Order Accurate Interface Tracking Algorithms and Improved Constitutive Models for Problems in Continuum Mechanics with Applications to Jetting' and with my CoPI on that grant Professor Greg Miller of the Department of Applied Science at UCD. In theory I tried to use funds from the SciDAC grant DE-FC02-01ER25473 to support work that directly involved implementing algorithms developed by my research group at U.C. Davis in software that was developed and is maintained by my SciDAC CoPI's at LBNL.