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An Implementation Framework for Solving High-Dimensional PDEs on Massively Parallel Computers

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Magnus Gustafsson

    (Uppsala University, Department of Information Technology)

  • Sverker Holmgren

    (Uppsala University, Department of Information Technology)

Abstract

Accurate solution of time-dependent, high-dimensional PDEs requires massive-scale parallel computing. In this paper, we describe an implementation framework for block-decomposed structured grids and discuss techniques for optimization on clusters where the nodes have one or more multicore processors. We use a two-level parallelization scheme with message passing between nodes and multithreading within each node, and argue that this is the best compromise for memory efficiency. We present some examples where the time-dependent Schrödinger equation is solved.

Suggested Citation

  • Magnus Gustafsson & Sverker Holmgren, 2010. "An Implementation Framework for Solving High-Dimensional PDEs on Massively Parallel Computers," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 417-424, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_44
    DOI: 10.1007/978-3-642-11795-4_44
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