#include <local_system.hh>

Public Member Functions
	LocalSystem ()
	Default constructor. More...

	LocalSystem (uint nrows, uint ncols)
	Constructor. More...

void	reset ()
	Resets the matrix, RHS, dofs to zero and clears solution settings. More...

void	reset (uint nrows, uint ncols)
	Resize and reset. More...

void	reset (const LocDofVec &row_dofs, const LocDofVec &col_dofs)

const arma::mat &	get_matrix ()

const arma::vec &	get_rhs ()

void	set_solution (uint loc_dof, double solution, double diag=0.0)
	Set the position and value of known solution. E.g. Dirichlet boundary condition. More...

void	set_solution_row (uint loc_row, double solution, double diag=0.0)

void	set_solution_col (uint loc_col, double solution)

void	eliminate_solution ()

void	add_value (uint row, uint col, double mat_val, double rhs_val)
	Adds a single entry into the local system. More...

void	add_value (uint row, uint col, double mat_val)
	Matrix entry. Adds a single entry into the local system matrix. More...

void	add_value (uint row, double rhs_val)
	RHS entry. Adds a single entry into the local system RHS. More...

void	set_matrix (arma::mat matrix)

void	set_rhs (arma::vec rhs)

void	set_sparsity (const arma::umat &sp)
	Sets the sparsity pattern for the local system. More...

void	compute_schur_complement (uint offset, LocalSystem &schur, bool negative=false) const
	Computes Schur complement of the local system: S = C - B * invA * Bt Applicable for square matrices. It can be called either after eliminating Dirichlet dofs, or the Dirichlet dofs can be set on the Schur complement and the elimination done on the Schur complement. More...

void	reconstruct_solution_schur (uint offset, const arma::vec &schur_solution, arma::vec &reconstructed_solution) const
	Reconstructs the solution from the Schur complement solution: x = invAb - invA Bt * schur_solution Applicable for square matrices. More...

Public Attributes
LocDofVec	row_dofs

LocDofVec	col_dofs

Protected Member Functions
void	set_size (uint nrows, uint ncols)

Protected Attributes
arma::mat	matrix
	local system matrix More...

arma::vec	rhs
	local system RHS More...

arma::mat	sparsity
	sparsity pattern More...

uint	n_elim_rows
	Number of rows/cols to be eliminated due to known solution. More...

uint	n_elim_cols

LocDofVec	elim_rows

LocDofVec	elim_cols
	Rows indices of rows to be eliminated. More...

arma::vec	solution_rows
	Cols indices of cols to be eliminated. More...

arma::vec	solution_cols
	Values of the known solution (for row dofs). More...

arma::vec	diag_rows
	Values of the known solution (for col dofs). More...

Static Protected Attributes
static constexpr double	almost_zero = std::numeric_limits<double>::min()
	Prefered values on the diagonal after elimination. More...

Friends
class	LinSys

Detailed Description

Local system class is meant to be used for local assembly and then pass to global linear system. The key idea is to take care of known solution values (Dirichlet boundary conditions) in a common way.

A] Usage of the class consists of 5 steps: 1) create local system, set local/global DoFs. 2) possibly setup sparsity pattern for the local system 3) set matrix and RHS entries 4) set all known values (Dirichlet BC) (the order of items 3 and 4 does not matter) 5) possibly eliminate the known solution (possibly fix the diagonal entries of the local system, where Dirichlet BC is set) 6) pass the local system to the global system, possibly with the map local_to_global

B] Scenario with computation of Schur complement: 1) do A1, do not have to set dof indices (if not doing B3) 2) do A2, A3 3) possibly do A4, A5, if there is known solution for the dofs not included in the Schur complement 3) create another LocalSystem for Schur complement (local_schur), possibly set dof indices 4) possibly do A2 on local_schur 4) compute Schur complement, passing the prepared local_schur 5) if not done before, set dof indices 6) possibly do A4, A5 on local_schur 7) do A6 with local_schur

C] Reconstruction from the Schur complement 1) do A1, A3 2) reconstruct the full solution

TODO:

set dofs as references
done: use arma::vec<int> to keep dofs (efficient, can be constructed from raw arrays)
done: use local dof indeces to set solution
rename set_solution to set_constraint

Definition at line 45 of file local_system.hh.

Constructor & Destructor Documentation

LocalSystem::LocalSystem ( )

Default constructor.

Object must be initialized by subsequent call of reset(nrows, ncols).

Definition at line 9 of file local_system.cc.

LocalSystem::LocalSystem	(	uint	nrows,
		uint	ncols
	)

Constructor.

nrows is number of rows of local system ncols is number of columns of local system

Definition at line 13 of file local_system.cc.

Member Function Documentation

void LocalSystem::add_value	(	uint	row,
		uint	col,
		double	mat_val,
		double	rhs_val
	)

Adds a single entry into the local system.

row is local row index of local system col is local column index of local system mat_val is matrix entry value rhs_val is RHS entry value

Definition at line 169 of file local_system.cc.

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void LocalSystem::add_value	(	uint	row,
		uint	col,
		double	mat_val
	)

Matrix entry. Adds a single entry into the local system matrix.

row is local row index of local system col is local column index of local system mat_val is matrix entry value

Definition at line 179 of file local_system.cc.

void LocalSystem::add_value	(	uint	row,
		double	rhs_val
	)

RHS entry. Adds a single entry into the local system RHS.

row is local row index of local system rhs_val is RHS entry value

Definition at line 188 of file local_system.cc.

void LocalSystem::compute_schur_complement	(	uint	offset,
		LocalSystem &	schur,
		bool	negative = `false`
	)		const

Computes Schur complement of the local system: S = C - B * invA * Bt Applicable for square matrices. It can be called either after eliminating Dirichlet dofs, or the Dirichlet dofs can be set on the Schur complement and the elimination done on the Schur complement.

offset index of the first row/column of submatrix C (size of A) schur (output) LocalSystem with Schur complement negative if true, the schur complement (including its rhs) is multiplied by -1.0

Definition at line 220 of file local_system.cc.

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void LocalSystem::eliminate_solution ( )

When finished with assembly of the local system, this function eliminates all the known dofs.

It is skipped if there is not any solution dof set.

During elimination, the (global) diagonal entries on the rows, where the solution is set, might be zero. Therefore it is necessary to set a proper value to the diagonal entry and respective RHS entry, such that the given solution holds. If preferred diagonal value has been set by set_solution then it is used.

Calling this function after the assembly of local system and before passing the local system to the global one is finished is users's responsibility.

Definition at line 102 of file local_system.cc.

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const arma::mat& LocalSystem::get_matrix ( )

inline

Definition at line 81 of file local_system.hh.

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const arma::vec& LocalSystem::get_rhs ( )

inline

Definition at line 82 of file local_system.hh.

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void LocalSystem::reconstruct_solution_schur	(	uint	offset,
		const arma::vec &	schur_solution,
		arma::vec &	reconstructed_solution
	)		const

Reconstructs the solution from the Schur complement solution: x = invA*b - invA * Bt * schur_solution Applicable for square matrices.

offset index of the first row/column of submatrix C (size of A) schur_solution solution of the Schur complement reconstructed_solution (output) reconstructed solution of the complementary variable

Definition at line 241 of file local_system.cc.

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void LocalSystem::reset ( )

Resets the matrix, RHS, dofs to zero and clears solution settings.

Definition at line 45 of file local_system.cc.

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void LocalSystem::reset	(	uint	nrows,
		uint	ncols
	)

Resize and reset.

Definition at line 55 of file local_system.cc.

void LocalSystem::reset	(	const LocDofVec &	row_dofs,
		const LocDofVec &	col_dofs
	)

Resize and reset. Set dofs vectors to reuse arrays provided by given vectors. Given vectors can not be changed until next call to of any reset function.

Definition at line 67 of file local_system.cc.

void LocalSystem::set_matrix ( arma::mat matrix )

Definition at line 196 of file local_system.cc.

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void LocalSystem::set_rhs ( arma::vec rhs )

Definition at line 202 of file local_system.cc.

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void LocalSystem::set_size	(	uint	nrows,
		uint	ncols
	)

protected

Definition at line 28 of file local_system.cc.

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void LocalSystem::set_solution	(	uint	loc_dof,
		double	solution,
		double	diag = `0.0`
	)

Set the position and value of known solution. E.g. Dirichlet boundary condition.

loc_dofs is local row index in solution vector solution is the values of the solution diag_val is preferred diagonal value on the solution row

Definition at line 81 of file local_system.cc.

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void LocalSystem::set_solution_col	(	uint	loc_col,
		double	solution
	)

Definition at line 96 of file local_system.cc.

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void LocalSystem::set_solution_row	(	uint	loc_row,
		double	solution,
		double	diag = `0.0`
	)

Definition at line 89 of file local_system.cc.

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void LocalSystem::set_sparsity ( const arma::umat & sp )

Sets the sparsity pattern for the local system.

Due to petsc options: MatSetOption(matrix_, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE) all zeros will be thrown away from the system. If we do not want some zero entries in the system matrix to be thrown away, we can set these entries with this almost zero value.

Almost_zero values will be set in all entries: sp(i,j) != 0

Definition at line 207 of file local_system.cc.

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Friends And Related Function Documentation

friend class LinSys

friend

Definition at line 203 of file local_system.hh.

Member Data Documentation

constexpr double LocalSystem::almost_zero = std::numeric_limits<double>::min()

staticprotected

Prefered values on the diagonal after elimination.

Due to petsc options: MatSetOption(matrix_, MAT_IGNORE_ZERO_ENTRIES, PETSC_TRUE) all zeros will be thrown away from the system. If we do not want some zero entries in the system matrix to be thrown away, we can set these entries with this almost zero value.

This is done for example when BC values are eliminated and later the BC changes to different type (e.g. seepage). Another case is keeping the structure of matrix unchanged for the schur complements - for that we fill the whole diagonal (escpecially block C in darcy flow) with artificial zeros.

Definition at line 200 of file local_system.hh.

LocDofVec LocalSystem::col_dofs

Definition at line 53 of file local_system.hh.

arma::vec LocalSystem::diag_rows

protected

Values of the known solution (for col dofs).

Definition at line 190 of file local_system.hh.

LocDofVec LocalSystem::elim_cols

protected

Rows indices of rows to be eliminated.

Definition at line 187 of file local_system.hh.

LocDofVec LocalSystem::elim_rows

protected

Definition at line 186 of file local_system.hh.

arma::mat LocalSystem::matrix

protected

local system matrix

Definition at line 179 of file local_system.hh.

uint LocalSystem::n_elim_cols

protected

Definition at line 185 of file local_system.hh.

uint LocalSystem::n_elim_rows

protected

Number of rows/cols to be eliminated due to known solution.

Definition at line 185 of file local_system.hh.

arma::vec LocalSystem::rhs

protected

local system RHS

Definition at line 180 of file local_system.hh.

LocDofVec LocalSystem::row_dofs

Global row and col indices. Are public and can be freely set. Nevertheless one can also provide reference to already existing arrays through specific constructor or reset function.

Definition at line 53 of file local_system.hh.

arma::vec LocalSystem::solution_cols

protected

Values of the known solution (for row dofs).

Definition at line 189 of file local_system.hh.

arma::vec LocalSystem::solution_rows

protected

Cols indices of cols to be eliminated.

Definition at line 188 of file local_system.hh.

arma::mat LocalSystem::sparsity

protected

sparsity pattern

Definition at line 182 of file local_system.hh.

The documentation for this class was generated from the following files:

/opt/flow123d/flow123d/src/la/local_system.hh
/opt/flow123d/flow123d/src/la/local_system.cc

Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Static Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation