'^ ^^^H^^^^r 



Clockwise from lower left, volume ren- 

 derings display the density of a bubble 

 being hit by a shock wave. New adap- 

 tive gridding and fast, accurate, and 

 robust numerical algonthms are used to 

 simulate the behavior of such highly 

 nonlinear fluid flows in complicated 

 three-dimensional geometries. These 

 techniques are implemented on the lat- 

 est vector and massively parallel archi- 

 tectures. Applied mathematicians and 

 computational scientists performed this 

 research at Lawrence Livermore 

 National Laboratory. Los Alamos 

 National Laboratory. New York 

 University, and the University of 

 California at Berkeley. 



number of fellowships was increased to 42 at 35 

 universities and institutes. This program and the 

 syllabus described above have been instrumental 

 in defining the discipline of computational science. 



Fundamental Research Programs 



The Applied Mathematics program supports a broad 

 range of activities at universities and DOE Laboratories 

 in modeling, analysis, and numerical simulation of physi- 

 cal and biological phenomena that arise in energy and 

 environmental systems. Most of the projects involve 

 applications-driven studies of the mathematical and 

 numerical tools required to understand the behavior of 

 complex discrete and continuous systems with an 

 emphasis on algorithms for parallel computing. It has 

 cofunded with NSF the Geometry Science and 

 Technology Center at the University of Minnesota to 

 apply new HPCC technology to traditional mathematics 

 problems. It has initiated new efforts in complex nonlin- 

 ear behavior that underlies most natural phenomena, 

 and in graph and group theories related to discrete phe- 

 nomena and topology for application to genome 

 sequencing and protein structure. 



In computer science the focus is on understanding how 

 parallel and distributed computer systems can be 

 applied more effectively to large-scale scientific prob- 

 lems. Supported projects include research in program- 

 ming models and tools, improved software libraries for 

 parallel computers, scientific visualization of large data 

 sets, software performance analysis techniques, and 

 message-passing utilities to facilitate distributed comput- 

 ing. 



FY 1994 Milestones 



HPCS 



Begin evaluating one or two additional early prototype 

 systems in cooperation with vendors. 



Expand computer systems performance analysis project, 

 including top-down algorithmic analysis of Grand 

 Challenge codes at HPCRCs. 



78 



