Definition of a nonlinear system of equations, r(u) = 0. More...

Detailed Description

Definition of a nonlinear system of equations, r(u) = 0.

Instead of directly defining a nonlinear system, we define the linearized system via its residual and Jacobian, evaluated at a given state u with given variables g, the linearized system is usually expressed as dr(u; g)/du * du = -r(u; g). Rewriting this in the more familiar form Au = b, we have A := dr(u; g)/du and b := -r(u; g).

Practically, this means that whenever u or g changes, we need to invalidate the system matrix A and RHS b, and recompute them when requested.

#include <NonlinearSystem.h>

Inheritance diagram for NonlinearSystem:

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Public Member Functions
void	u_changed () override
	Trigger when unknown variables changed.
	LinearSystem ()=default
	LinearSystem (const LinearSystem &)=default
	LinearSystem (LinearSystem &&) noexcept=default
Public Member Functions inherited from LinearSystem
	LinearSystem ()=default
	LinearSystem (const LinearSystem &)=default
	LinearSystem (LinearSystem &&) noexcept=default
LinearSystem &	operator= (const LinearSystem &)=default
LinearSystem &	operator= (LinearSystem &&) noexcept=default
virtual	~LinearSystem ()=default
virtual void	init ()
std::size_t	m () const
	Number of rows in the matrix.
std::size_t	n () const
	Number of columns in the matrix.
std::size_t	p () const
	Number of columns in the auxiliary matrix.
virtual void	set_u (const SparseTensorList &)=0
	Set the unknown u.
virtual void	set_g (const SparseTensorList &)=0
	Set the given variables g from the current step.
virtual SparseTensorList	u () const =0
	Get the unknown u.
virtual SparseTensorList	g () const =0
	Get the given variables g from the current step.
virtual void	g_changed ()
	Trigger when given variables changed.
SparseTensorList	A ()
	Assemble and return the operator, A.
SparseTensorList	b ()
	Assemble and return the right-hand side, b.
std::tuple< SparseTensorList, SparseTensorList >	A_and_b ()
	Assemble and return the right-hand side and operator.
std::tuple< SparseTensorList, SparseTensorList >	A_and_B ()
	Assemble the auxiliary matrix B = dr/dg along with A.
std::tuple< SparseTensorList, SparseTensorList, SparseTensorList >	A_and_B_and_b ()
	Assemble the auxiliary matrix B = dr/dg along with A and b.
const std::vector< LabeledAxisAccessor > &	umap () const
	Get the ID-to-unknown mapping for assembly.
const std::vector< TensorShape > &	intmd_ulayout () const
	Get the ID-to-unknown-intermediate-shape mapping for assembly.
const std::vector< TensorShape > &	ulayout () const
	Get the ID-to-unknown-base-shape mapping for assembly.
const std::vector< LabeledAxisAccessor > &	gmap () const
	Get the ID-to-prescribed-variable mapping for assembly.
const std::vector< TensorShape > &	intmd_glayout () const
	Get the ID-to-prescribed-variable-intermediate-shape mapping for assembly.
const std::vector< TensorShape > &	glayout () const
	Get the ID-to-prescribed-variable-base-shape mapping for assembly.
const std::vector< LabeledAxisAccessor > &	bmap () const
	Get the ID-to-RHS mapping for assembly.
const std::vector< TensorShape > &	intmd_blayout () const
	Get the ID-to-RHS-intermediate-shape mapping for assembly.
const std::vector< TensorShape > &	blayout () const
	Get the ID-to-RHS-base-shape mapping for assembly.

Additional Inherited Members
Protected Member Functions inherited from LinearSystem
virtual std::vector< LabeledAxisAccessor >	setup_umap ()=0
	Setup the unknown map.
virtual std::vector< TensorShape >	setup_intmd_ulayout ()=0
	Setup the unknown intermediate layout.
virtual std::vector< TensorShape >	setup_ulayout ()=0
	Setup the unknown layout.
virtual std::vector< LabeledAxisAccessor >	setup_gmap ()=0
	Setup the given variable map.
virtual std::vector< TensorShape >	setup_intmd_glayout ()=0
	Setup the given variable intermediate layout.
virtual std::vector< TensorShape >	setup_glayout ()=0
	Setup the given variable base layout.
virtual std::vector< LabeledAxisAccessor >	setup_bmap ()=0
	Setup the RHS map.
virtual std::vector< TensorShape >	setup_intmd_blayout ()=0
	Setup the RHS intermediate layout.
virtual std::vector< TensorShape >	setup_blayout ()=0
	Setup the RHS layout.
virtual void	assemble (SparseTensorList A, SparseTensorList B, SparseTensorList *b)=0
	Compute the operator and right-hand side.
virtual void	pre_assemble (bool A, bool B, bool b)
	Callback before assembly to perform.
virtual void	post_assemble (bool A, bool B, bool b)
	Callback after assembly to perform.
Protected Attributes inherited from LinearSystem
bool	_A_up_to_date = false
	Flag indicating if the system matrix is up to date. Setters invalidate this.
bool	_B_up_to_date = false
	Flag indicating if the auxiliary matrix is up to date. Setters invalidate this.
bool	_b_up_to_date = false
	Flag indicating if the system RHS is up to date. Setters invalidate this.
std::vector< LabeledAxisAccessor >	_umap
	The ID-to-unknown mapping.
std::optional< std::vector< TensorShape > >	_intmd_ulayout
	ID-to-unknown intermediate shape mapping.
std::vector< TensorShape >	_ulayout
	ID-to-unknown base shape mapping.
std::vector< LabeledAxisAccessor >	_gmap
	The ID-to-given-variable mapping.
std::optional< std::vector< TensorShape > >	_intmd_glayout
	ID-to-given intermediate shape mapping.
std::vector< TensorShape >	_glayout
	ID-to-given base shape mapping.
std::vector< LabeledAxisAccessor >	_bmap
	The ID-to-RHS mapping.
std::optional< std::vector< TensorShape > >	_intmd_blayout
	ID-to-RHS intermediate shape mapping.
std::vector< TensorShape >	_blayout
	ID-to-RHS shape mapping.

Member Function Documentation

◆ LinearSystem() [1/3]

LinearSystem ( )

default

◆ LinearSystem() [2/3]

LinearSystem ( const LinearSystem & )

default

◆ LinearSystem() [3/3]

LinearSystem ( LinearSystem && )

defaultnoexcept

◆ u_changed()

void u_changed ( )

overridevirtual

Trigger when unknown variables changed.

Reimplemented from LinearSystem.