Rodin::Geometry::Shard class
#include <Rodin/Geometry/Shard.h>

Advanced mesh shard for distributed parallel computing.

A Shard is a specialized mesh that represents a portion of a larger mesh in a distributed computing context. Unlike the simplified MeshShard, this class provides full support for ghost polytopes and ownership tracking, which are essential for parallel finite element computations.

Distributed Computing Concepts

In parallel mesh decomposition, each process owns a subset of mesh elements:

  • Owned polytopes: Elements that this process is responsible for computing
  • Ghost polytopes: Elements owned by other processes but needed for boundary computations
  • Halo: The set of processes that need ghost information from this shard

Mathematical Foundation

For a mesh $ \mathcal{T}_h $ decomposed into $ N $ shards:

\[ \mathcal{T}_h = \bigcup_{i=1}^{N} \mathcal{S}_i \]

where each shard $ \mathcal{S}_i $ contains both owned and ghost elements.

Usage in MPI Applications

// Build a shard from a parent mesh
Shard::Builder builder;
builder.initialize(parentMesh);

// Include owned polytopes
for (Index idx : ownedCells)
  builder.include({dimension, idx}, Shard::Flags::Owned);

// Include ghost polytopes from neighboring processes
for (Index idx : ghostCells)
  builder.include({dimension, idx}, Shard::Flags::Ghost);

Shard shard = builder.finalize();

// Check polytope ownership
if (shard.isOwned(d, localIdx))
  // Compute on this element

Thread Safety

Shard objects are not thread-safe during construction. Once finalized, read-only operations are thread-safe.

Base classes

template<>
class Mesh<Context::Local>
Represents the subdivision of some domain into faces of (possibly) different geometries.

Public types

class Builder
Builder for constructing Shard instances.
class Flags
Bitmask flags indicating polytope state.
struct PolytopeMap
Bidirectional polytope index mapping.
using ContextType = Rodin::Context::Local
Context type (always local for shards).
using Parent = Mesh<ContextType>
Parent mesh type.

Constructors, destructors, conversion operators

Shard() defaulted
Default constructor.
Shard(const Shard& other)
Copy constructor.
Shard(Shard&& other)
Move constructor.

Public functions

auto operator=(Shard&& other) -> Shard&
Move assignment operator.
auto isGhost(size_t d, Index idx) const -> bool
Checks if a polytope is a ghost element.
auto isOwned(size_t d, Index idx) const -> bool
Checks if a polytope is owned by this shard.
auto getOwner(size_t d) const -> const FlatMap<Index, Index>&
Gets the owner map for a dimension.
auto getHalo(size_t d) const -> const FlatMap<Index, IndexSet>&
Gets the halo map for a dimension.
auto getPolytopeMap(size_t d) const -> const PolytopeMap&
Gets the polytope index map for a dimension.
template<class Archive>
void serialize(Archive& ar, const unsigned int version)
Serialization method for Boost.Serialization.

Function documentation

Rodin::Geometry::Shard::Shard(const Shard& other)

Copy constructor.

Parameters
other in Shard to copy from

Rodin::Geometry::Shard::Shard(Shard&& other)

Move constructor.

Parameters
other in Shard to move from

Shard& Rodin::Geometry::Shard::operator=(Shard&& other)

Move assignment operator.

Parameters
other in Shard to move from
Returns Reference to this object

bool Rodin::Geometry::Shard::isGhost(size_t d, Index idx) const

Checks if a polytope is a ghost element.

Parameters
d in Dimension of the polytope
idx in Local index of the polytope
Returns True if the polytope is ghosted from another process

Ghost elements are owned by another process but included in this shard for boundary calculations.

bool Rodin::Geometry::Shard::isOwned(size_t d, Index idx) const

Checks if a polytope is owned by this shard.

Parameters
d in Dimension of the polytope
idx in Local index of the polytope
Returns True if the polytope is owned by this process

Owned elements are those this process is responsible for computing.

const FlatMap<Index, Index>& Rodin::Geometry::Shard::getOwner(size_t d) const

Gets the owner map for a dimension.

Parameters
d in Dimension
Returns Map from ghost polytope index to owning process ID

const FlatMap<Index, IndexSet>& Rodin::Geometry::Shard::getHalo(size_t d) const

Gets the halo map for a dimension.

Parameters
d in Dimension
Returns Map from owned polytope index to set of processes needing it

The halo identifies which neighboring processes need ghost copies of this shard's owned elements.

const PolytopeMap& Rodin::Geometry::Shard::getPolytopeMap(size_t d) const

Gets the polytope index map for a dimension.

Parameters
d in Dimension
Returns Bidirectional mapping between shard and parent indices

template<class Archive>
void Rodin::Geometry::Shard::serialize(Archive& ar, const unsigned int version)

Serialization method for Boost.Serialization.

Template parameters
Archive Archive type
Parameters
ar in/out Archive object
version in Serialization version