Terascale Optimal PDE Simulations (TOPS) Center

Widlund, Olof B

doi:10.2172/909572

Title: Terascale Optimal PDE Simulations (TOPS) Center

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Abstract

Our work has focused on the development and analysis of domain decomposition algorithms for a variety of problems arising in continuum mechanics modeling. In particular, we have extended and analyzed FETI-DP and BDDC algorithms; these iterative solvers were first introduced and studied by Charbel Farhat and his collaborators, see [11, 45, 12], and by Clark Dohrmann of SANDIA, Albuquerque, see [43, 2, 1], respectively. These two closely related families of methods are of particular interest since they are used more extensively than other iterative substructuring methods to solve very large and difficult problems. Thus, the FETI algorithms are part of the SALINAS system developed by the SANDIA National Laboratories for very large scale computations, and as already noted, BDDC was first developed by a SANDIA scientist, Dr. Clark Dohrmann. The FETI algorithms are also making inroads in commercial engineering software systems. We also note that the analysis of these algorithms poses very real mathematical challenges. The success in developing this theory has, in several instances, led to significant improvements in the performance of these algorithms. A very desirable feature of these iterative substructuring and other domain decomposition algorithms is that they respect the memory hierarchy of modern parallel and distributedmore »« less

Authors:: Widlund, Olof B

Publication Date:: Mon Jul 09 00:00:00 EDT 2007

Research Org.:: New York University, Courant Institute

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 909572

Report Number(s):: DOE/ER/25482-1
TRN: US200816%%657

DOE Contract Number:: FC02-01ER25482

Resource Type:: Technical Report

Country of Publication:: United States

Language:: English

Subject:: 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; COMPUTERS; DIMENSIONS; ITERATIVE METHODS; PERFORMANCE; RESOLUTION; SANDIA NATIONAL LABORATORIES; SIMULATION; numerical analysis, parallel computing, partial differential equations, continuum mechanics

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                    Widlund, Olof B. Terascale Optimal PDE Simulations (TOPS) Center.  United States: N. p., 2007. 
        Web.  doi:10.2172/909572.

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                    Widlund, Olof B. Terascale Optimal PDE Simulations (TOPS) Center.  United States.  https://doi.org/10.2172/909572

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                    Widlund, Olof B. 2007.  
        "Terascale Optimal PDE Simulations (TOPS) Center".  United States.  https://doi.org/10.2172/909572.  https://www.osti.gov/servlets/purl/909572.

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@article{osti_909572,

  title        = {Terascale Optimal PDE Simulations (TOPS) Center},

  author       = {Widlund, Olof B},

  abstractNote = {Our work has focused on the development and analysis of domain decomposition algorithms for a variety of problems arising in continuum mechanics modeling. In particular, we have extended and analyzed FETI-DP and BDDC algorithms; these iterative solvers were first introduced and studied by Charbel Farhat and his collaborators, see [11, 45, 12], and by Clark Dohrmann of SANDIA, Albuquerque, see [43, 2, 1], respectively. These two closely related families of methods are of particular interest since they are used more extensively than other iterative substructuring methods to solve very large and difficult problems. Thus, the FETI algorithms are part of the SALINAS system developed by the SANDIA National Laboratories for very large scale computations, and as already noted, BDDC was first developed by a SANDIA scientist, Dr. Clark Dohrmann. The FETI algorithms are also making inroads in commercial engineering software systems. We also note that the analysis of these algorithms poses very real mathematical challenges. The success in developing this theory has, in several instances, led to significant improvements in the performance of these algorithms. A very desirable feature of these iterative substructuring and other domain decomposition algorithms is that they respect the memory hierarchy of modern parallel and distributed computing systems, which is essential for approaching peak floating point performance. The development of improved methods, together with more powerful computer systems, is making it possible to carry out simulations in three dimensions, with quite high resolution, relatively easily. This work is supported by high quality software systems, such as Argonne's PETSc library, which facilitates code development as well as the access to a variety of parallel and distributed computer systems. The success in finding scalable and robust domain decomposition algorithms for very large number of processors and very large finite element problems is, e.g., illustrated in [24, 25, 26]. This work is based on [29, 31]. Our work over these five and half years has, in our opinion, helped advance the knowledge of domain decomposition methods significantly. We see these methods as providing valuable alternatives to other iterative methods, in particular, those based on multi-grid. In our opinion, our accomplishments also match the goals of the TOPS project quite closely.},

  doi          = {10.2172/909572},

  url          = {https://www.osti.gov/biblio/909572},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {Mon Jul 09 00:00:00 EDT 2007},

  month        = {Mon Jul 09 00:00:00 EDT 2007}

}

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