#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 = invA*b - 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.
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
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.
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.
| 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.
|
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 241 of file local_system.cc.
| void LocalSystem::reset | ( | ) |
Resets the matrix, RHS, dofs to zero and clears solution settings.
Definition at line 45 of file local_system.cc.
Resize and reset.
Definition at line 55 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 67 of file local_system.cc.
| void LocalSystem::set_matrix | ( | arma::mat | matrix | ) |
| void LocalSystem::set_rhs | ( | arma::vec | rhs | ) |
| 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.
| 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 207 of file local_system.cc.
Friends And Related Function Documentation
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friend |
Definition at line 203 of file local_system.hh.
Member Data Documentation
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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.
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protected |
Values of the known solution (for col dofs).
Definition at line 190 of file local_system.hh.
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protected |
Rows indices of rows to be eliminated.
Definition at line 187 of file local_system.hh.
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protected |
Definition at line 186 of file local_system.hh.
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protected |
local system matrix
Definition at line 179 of file local_system.hh.
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protected |
Definition at line 185 of file local_system.hh.
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protected |
Number of rows/cols to be eliminated due to known solution.
Definition at line 185 of file local_system.hh.
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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.
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protected |
Values of the known solution (for row dofs).
Definition at line 189 of file local_system.hh.
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protected |
Cols indices of cols to be eliminated.
Definition at line 188 of file local_system.hh.
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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
