Flow123d
master-f44eb46
|
#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 (LocalConstraint &loc_constraint) |
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 = invA*b - invA * Bt * schur_solution Applicable for square matrices. More... | |
Public Attributes | |
LocDofVec | row_dofs |
LocDofVec | col_dofs |
Static Public Attributes | |
static constexpr double | almost_zero = std::numeric_limits<double>::min() |
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... | |
Friends | |
class | LinSys |
Prefered values on the diagonal after elimination. More... | |
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:
Definition at line 46 of file local_system.hh.
LocalSystem::LocalSystem | ( | ) |
Default constructor.
Object must be initialized by subsequent call of reset(nrows, ncols).
Definition at line 10 of file local_system.cc.
Constructor.
nrows
is number of rows of local system ncols
is number of columns of local system
Definition at line 14 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 197 of file local_system.cc.
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 188 of file local_system.cc.
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 178 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 229 of file local_system.cc.
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 111 of file local_system.cc.
|
inline |
|
inline |
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 250 of file local_system.cc.
void LocalSystem::reset | ( | ) |
Resets the matrix, RHS, dofs to zero and clears solution settings.
Definition at line 46 of file local_system.cc.
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 68 of file local_system.cc.
Resize and reset.
Definition at line 56 of file local_system.cc.
void LocalSystem::set_matrix | ( | arma::mat | matrix | ) |
void LocalSystem::set_rhs | ( | arma::vec | rhs | ) |
void LocalSystem::set_solution | ( | LocalConstraint & | loc_constraint | ) |
Set the position and value of known solution. E.g. Dirichlet boundary condition.
LocalConstraint
data object holds all needed data used in previous method
Definition at line 90 of file local_system.cc.
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 82 of file local_system.cc.
void LocalSystem::set_solution_col | ( | uint | loc_col, |
double | solution | ||
) |
void LocalSystem::set_solution_row | ( | uint | loc_row, |
double | solution, | ||
double | diag = 0.0 |
||
) |
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 216 of file local_system.cc.
|
friend |
Prefered values on the diagonal after elimination.
Definition at line 212 of file local_system.hh.
|
staticconstexpr |
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 191 of file local_system.hh.
LocDofVec LocalSystem::col_dofs |
Definition at line 54 of file local_system.hh.
|
protected |
Values of the known solution (for col dofs).
Definition at line 208 of file local_system.hh.
|
protected |
Rows indices of rows to be eliminated.
Definition at line 205 of file local_system.hh.
|
protected |
Definition at line 204 of file local_system.hh.
|
protected |
local system matrix
Definition at line 197 of file local_system.hh.
|
protected |
Definition at line 203 of file local_system.hh.
|
protected |
Number of rows/cols to be eliminated due to known solution.
Definition at line 203 of file local_system.hh.
|
protected |
local system RHS
Definition at line 198 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 54 of file local_system.hh.
|
protected |
Values of the known solution (for row dofs).
Definition at line 207 of file local_system.hh.
|
protected |
Cols indices of cols to be eliminated.
Definition at line 206 of file local_system.hh.
|
protected |
sparsity pattern
Definition at line 200 of file local_system.hh.