From: Martin Kronbichler Date: Fri, 3 Jun 2022 08:42:45 +0000 (+0200) Subject: Document possibility for data locality in matrix-free tutorial X-Git-Tag: v9.4.0-rc1~75^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F13899%2Fhead;p=dealii.git Document possibility for data locality in matrix-free tutorial --- diff --git a/examples/step-37/doc/results.dox b/examples/step-37/doc/results.dox index 7ef0edf09b..776ca401cb 100644 --- a/examples/step-37/doc/results.dox +++ b/examples/step-37/doc/results.dox @@ -675,3 +675,28 @@ object. Doing this would require making substantial modifications to the LaplaceOperator class, but the MatrixFreeOperators::LaplaceOperator class that comes with the library can do this. See the discussion on blocks in MatrixFreeOperators::Base for more information on how to set up blocks. + +

Further performance improvements

+ +While the performance achieved in this tutorial program is already very good, +there is functionality in deal.II to further improve the performance. On the +one hand, increasing the polynomial degree to three or four will further +improve the time per unknown. (Even higher degrees typically get slower again, +because the multigrid iteration counts increase slightly with the chosen +simple smoother. One could then use hybrid multigrid algorithms to use +polynomial coarsening through MGTransferGlobalCoarsening, to reduce the impact +of the coarser level on the communication latency.) A more significant +improvement can be obtained by data-locality optimizations. The class +PreconditionChebyshev, when combined with a `DiagonalMatrix` inner +preconditioner as in the present class, can overlap the vector operations with +the matrix-vector product. As the former are typically constrained by memory +bandwidth, reducing the number of loads helps to achieve this goal. The two +ingredients to achieve this are +
    +
  1. to provide LaplaceOperator class of this tutorial program with a `vmult` +function that takes two `std::function` objects, which can be passed on to +MatrixFree::cell_loop with the respective signature (PreconditionChebyshev +will then pick up this interface and schedule its vector operations), and
    2. +
  2. to compute a numbering that optimizes for data locality, as provided by +DoFRenumbering::matrix_free_data_locality().
    3. +