Line data    Source code

       1           0 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : #pragma once
       5             : 
       6             : #include <array>
       7             : #include <cstddef>
       8             : #include <optional>
       9             : #include <unordered_map>
      10             : #include <unordered_set>
      11             : #include <utility>
      12             : #include <vector>
      13             : 
      14             : template <size_t Dim>
      15             : class Block;
      16             : 
      17             : template <size_t Dim>
      18             : class ElementId;
      19             : 
      20           1 : namespace Spectral {
      21             : enum class Quadrature;
      22             : }  // namespace Spectral
      23             : 
      24             : namespace domain {
      25             : /// The weighting scheme for assigning computational costs to `Element`s for
      26             : /// distributing balanced compuational costs per processor (see
      27             : /// `BlockZCurveProcDistribution`)
      28           1 : enum class ElementWeight {
      29             :   /// A weighting scheme where each `Element` is assigned the same computational
      30             :   /// cost
      31             :   Uniform,
      32             :   /// A weighting scheme where each `Element`'s computational cost is equal to
      33             :   /// the number of grid points in that `Element`
      34             :   NumGridPoints,
      35             :   /// A weighting scheme where each `Element`'s computational cost is weighted
      36             :   /// by both the number of grid points and minimum spacing between grid points
      37             :   /// in that `Element` (see `get_num_points_and_grid_spacing_cost()` for
      38             :   /// details)
      39             :   NumGridPointsAndGridSpacing
      40             : };
      41             : 
      42             : /// \brief Get the cost of each `Element` in a list of `Block`s where
      43             : /// `element_weight` specifies which weight distribution scheme to use
      44             : ///
      45             : /// \details It is only necessary to pass in a value for `quadrature` if
      46             : /// the value for `element_weight` is
      47             : /// `ElementWeight::NumGridPointsAndGridSpacing`. Otherwise, the argument isn't
      48             : /// needed and will have no effect if it does have a value.
      49             : template <size_t Dim>
      50           1 : std::unordered_map<ElementId<Dim>, double> get_element_costs(
      51             :     const std::vector<Block<Dim>>& blocks,
      52             :     const std::vector<std::array<size_t, Dim>>& initial_refinement_levels,
      53             :     const std::vector<std::array<size_t, Dim>>& initial_extents,
      54             :     ElementWeight element_weight,
      55             :     const std::optional<Spectral::Quadrature>& quadrature);
      56             : 
      57             : /*!
      58             :  * \brief Distribution strategy for assigning elements to CPUs using a
      59             :  * Morton ('Z-order') space-filling curve to determine placement within each
      60             :  * block, where `Element`s are distributed across CPUs
      61             :  *
      62             :  * \details The element distribution attempts to assign a balanced total
      63             :  * computational cost to each processor that is allowed to have `Element`s.
      64             :  * First, each `Block`'s `Element`s are ordered by their Z-curve index (see more
      65             :  * below). `Element`s are traversed in this order and assigned to CPUs in order,
      66             :  * moving onto the next CPU once the target cost per CPU is met. The target cost
      67             :  * per CPU is defined as the remaining cost to distribute divided by the
      68             :  * remaining number of CPUs to distribute to. This is an important distinction
      69             :  * from simply having one constant target cost per CPU defined as the total cost
      70             :  * divided by the total number of CPUs with elements. Since the total cost of
      71             :  * `Element`s on a processor will nearly never add up to be exactly the average
      72             :  * cost per CPU, this means that we would either have to decide to overshoot or
      73             :  * undershoot the average as we iterate over the CPUs and assign `Element`s. If
      74             :  * we overshoot the average on each processor, the final processor could have a
      75             :  * much lower cost than the rest of the processors and we run the risk of
      76             :  * overshooting so much that one or more of the requested processors don't get
      77             :  * assigned any `Element`s at all. If we undershoot the average on each
      78             :  * processor, the final processor could have a much higher cost than the others
      79             :  * due to remainder cost piling up. This algorithm avoids these risks by instead
      80             :  * adjusting the target cost per CPU as we finish assigning cost to previous
      81             :  * CPUs.
      82             :  *
      83             :  * Morton curves are a simple and easily-computed space-filling curve that
      84             :  * (unlike Hilbert curves) permit diagonal traversal. See, for instance,
      85             :  * \cite Borrell2018 for a discussion of mesh partitioning using space-filling
      86             :  * curves.
      87             :  * A concrete example of the use of a Morton curve in 2d is given below.
      88             :  *
      89             :  * A sketch of a 2D block with 4x2 elements, with each element labeled according
      90             :  * to the order on the Morton curve:
      91             :  * ```
      92             :  *          x-->
      93             :  *          0   1   2   3
      94             :  *        ----------------
      95             :  *  y  0 |  0   2   4   6
      96             :  *  |    |  | / | / | / |
      97             :  *  v  1 |  1   3   5   7
      98             :  * ```
      99             :  * (forming a zig-zag path, that under some rotation/reflection has a 'Z'
     100             :  * shape).
     101             :  *
     102             :  * The Morton curve method is a quick way of getting acceptable spatial locality
     103             :  * -- usually, for approximately even distributions, it will ensure that
     104             :  * elements are assigned in large volume chunks, and the structure of the Morton
     105             :  * curve ensures that for a given processor and block, the elements will be
     106             :  * assigned in no more than two orthogonally connected clusters. In principle, a
     107             :  * Hilbert curve could potentially improve upon the gains obtained by this class
     108             :  * by guaranteeing that all elements within each block form a single
     109             :  * orthogonally connected cluster.
     110             :  *
     111             :  * The assignment of portions of blocks to processors may use partial blocks,
     112             :  * and/or multiple blocks to ensure an even distribution of elements to
     113             :  * processors.
     114             :  * We currently make no distinction between dividing elements between processors
     115             :  * within a node and dividing elements between processors across nodes. The
     116             :  * current technique aims to have a simple method of reducing communication
     117             :  * globally, though it would likely be more efficient to prioritize minimization
     118             :  * of inter-node communication, because communication across interconnects is
     119             :  * the primary cost of communication in charm++ runs.
     120             :  *
     121             :  * \warning The use of the Morton curve to generate a well-clustered element
     122             :  * distribution currently assumes that the refinement is uniform over each
     123             :  * block, with no internal structure that would be generated by, for instance
     124             :  * AMR.
     125             :  * This distribution method will need alteration to perform well for blocks with
     126             :  * internal structure from h-refinement. Morton curves can be defined
     127             :  * recursively, so a generalization of the present method is possible for blocks
     128             :  * with internal refinement
     129             :  *
     130             :  * \tparam Dim the number of spatial dimensions of the `Block`s
     131             :  */
     132             : template <size_t Dim>
     133           1 : struct BlockZCurveProcDistribution {
     134             :   /// The `number_of_procs_with_elements` argument represents how many procs
     135             :   /// will have elements. This is not necessarily equal to the total number of
     136             :   /// procs because some global procs may be ignored by the sixth argument
     137             :   /// `global_procs_to_ignore`.
     138           1 :   BlockZCurveProcDistribution(
     139             :       const std::unordered_map<ElementId<Dim>, double>& element_costs,
     140             :       size_t number_of_procs_with_elements,
     141             :       const std::vector<Block<Dim>>& blocks,
     142             :       const std::vector<std::array<size_t, Dim>>& initial_refinement_levels,
     143             :       const std::vector<std::array<size_t, Dim>>& initial_extents,
     144             :       const std::unordered_set<size_t>& global_procs_to_ignore = {});
     145             : 
     146             :   /// Gets the suggested processor number for a particular `ElementId`,
     147             :   /// determined by the Morton curve weighted element assignment described in
     148             :   /// detail in the parent class documentation.
     149           1 :   size_t get_proc_for_element(const ElementId<Dim>& element_id) const;
     150             : 
     151             :   const std::vector<std::vector<std::pair<size_t, size_t>>>&
     152           0 :   block_element_distribution() const {
     153             :     return block_element_distribution_;
     154             :   }
     155             : 
     156             :  private:
     157             :   // in this nested data structure:
     158             :   // - The block id is the first index
     159             :   // - There is an arbitrary number of CPUs per block, each with an element
     160             :   //   allowance
     161             :   // - Each element allowance is represented by a pair of proc number, number of
     162             :   //   elements in the allowance
     163             :   std::vector<std::vector<std::pair<size_t, size_t>>>
     164           0 :       block_element_distribution_;
     165             : };
     166             : }  // namespace domain