Rodin::Variational::Integrator class
#include <Rodin/Variational/Integrator.h>

Abstract base class for integrators in variational formulations.

The Integrator class provides a common interface for all types of integrators used in finite element assembly. Integrators compute local (element-level) contributions that are then assembled into global matrices and vectors.

Integrator Types

There are two main types of integrators:

  • Linear Integrators: Compute contributions to the load vector (RHS)
    • Example: $ b_i = \int_K f \psi_i \, dx $
  • Bilinear Integrators: Compute contributions to the system matrix
    • Example: $ A_{ij} = \int_K \nabla \phi_j \cdot \nabla \psi_i \, dx $

Role in Assembly

During the assembly process:

  1. Integrators are iterated over mesh elements
  2. Local contributions are computed using numerical quadrature
  3. Local contributions are mapped to global indices
  4. Global matrix/vector is updated with local contributions

Base classes

class Base
Base class for all objects in Rodin's FormLanguage system.

Public types

enum class Type { Linear, Bilinear }
Enumeration of integrator types.
using Parent = FormLanguage::Base
Parent class type.
using OrderType = std::function<size_t(const Geometry::Polytope&)>
Virtual destructor.

Constructors, destructors, conversion operators

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

Public functions

auto setOrder(std::nullopt_t) -> Integrator&
Restores order inference from the integrand.
auto setOrder(size_t order) -> Integrator&
Sets a constant integration order.
auto setOrder(OrderType order) -> Integrator&
Sets a rule computing the integration order per polytope.
auto getOrder(const Geometry::Polytope& polytope) const -> Optional<size_t>
The integration order to use on a polytope.
auto getType() const -> Type pure virtual
Gets the type of this integrator.
auto copy() const -> Integrator* override noexcept
Creates a copy of this integrator.

Enum documentation

enum class Rodin::Variational::Integrator::Type

Enumeration of integrator types.

Enumerators
Linear

Linear form integrator (load vector)
Bilinear

Bilinear form integrator (system matrix)

Typedef documentation

using Rodin::Variational::Integrator::OrderType = std::function<size_t(const Geometry::Polytope&)>

Virtual destructor.

Rule giving the integration order to use on a polytope.

Function documentation

Rodin::Variational::Integrator::Integrator(const Integrator& other)

Copy constructor.

Parameters
other in Integrator to copy

Rodin::Variational::Integrator::Integrator(Integrator&& other)

Move constructor.

Parameters
other in Integrator to move

Integrator& Rodin::Variational::Integrator::setOrder(std::nullopt_t)

Restores order inference from the integrand.

This is the default: the order is derived per polytope from the polynomial degrees of the finite elements living on it. Correct whenever the integrand is polynomial.

Integrator& Rodin::Variational::Integrator::setOrder(size_t order)

Sets a constant integration order.

Parameters
order in Integration order to use on every polytope

Note that the inferred order is a function of the polytope, so a constant is only equivalent to inference on a mesh whose elements all share one degree; prefer setOrder(OrderType) otherwise.

Integrator& Rodin::Variational::Integrator::setOrder(OrderType order)

Sets a rule computing the integration order per polytope.

Parameters
order in Rule invoked with the polytope being integrated

On an integrator the order is the degree of the quadrature rule, not the polynomial degree of an expression; the two coincide only when the integrand is polynomial. Set it explicitly whenever it is not — a coefficient composing a level set with a mesh lookup, say — since the inferred order is then meaningless and typically too low.

Optional<size_t> Rodin::Variational::Integrator::getOrder(const Geometry::Polytope& polytope) const

The integration order to use on a polytope.

Parameters
polytope in Polytope being integrated
Returns The order given by the rule, or an empty optional when the order is to be inferred from the integrand.

Type Rodin::Variational::Integrator::getType() const pure virtual

Gets the type of this integrator.

Returns Type indicating whether this is a linear or bilinear integrator

Integrator* Rodin::Variational::Integrator::copy() const override noexcept

Creates a copy of this integrator.

Returns Pointer to newly allocated copy