PolytopeQuadrature.h file

Cached quadrature data attached to mesh polytopes.

This file defines:

Rodin::Geometry::PolytopeQuadrature, which stores the mapped quadrature points associated with a specific quadrature formula on a specific polytope.
Rodin::Geometry::PolytopeQuadratureIndex, a mesh-owned, thread-safe cache indexed by polytope dimension, polytope index, and quadrature formula identity.

Purpose

Reference quadrature formulas belong to the Rodin::QF module and live on reference polytopes. In contrast, this file provides a geometry-side cache of their realization on concrete mesh polytopes.

For a polytope and a reference quadrature formula , the realized quadrature consists of the mapped geometric points:

where is the polytope transformation.

Cache organization

The cache is organized as:

where:

is the polytope dimension,
is the polytope index within that dimension.

Each slot stores:

one hot entry for the fastest repeated-hit access path,
one small bounded ring buffer of owned cached quadratures.

Lookup order is:

hot entry,
bounded per-slot cache,
lazy construction on miss.

Hits in the bounded cache are promoted to the hot slot. Misses are inserted into the bounded cache in round-robin order and then promoted to the hot slot.

Key

The cache key is the address of the quadrature formula object:

This design assumes that callers obtain quadrature formulas from a canonical source such as Rodin::QF::PolytopeQuadratureFormula::get, so that the same logical formula has a stable object identity.

Namespaces

namespace Rodin: The Rodin library for finite element methods and shape optimization.
namespace Rodin::Geometry: Module for dealing with meshes, polytopes, and geometric operations.

Classes

class Rodin::Geometry::PolytopeQuadrature: Cached quadrature attached to one specific polytope.
class Rodin::Geometry::PolytopeQuadratureIndex: Thread-safe cache of polytope quadratures.