Kratos lspg hrom

[SADPR]

Description

​The main developments for enabling the LSPG HROM involved the inclusion of a set of complementary elements and conditions corresponding to the HROM selected subset of elements and conditions.

In essence, the HROM LSPG is first assembled by iterating over the subset of HROM selected elements and multiplying them by positive weights. This results in the system:
$$J_h \Phi q = - R_h $$
For LSPG projection, we multiply by a left Reduced Order Basis (ROB), defined as:
$$\Psi = J_{c} \Phi $$
Here, $J_c$​ is assembled with the subset of HROM selected elements plus the complementary mesh, i.e., the neighboring nodes of this subset. After constructing $J_c$ , it's essential to zero out the degrees of freedom that are not part of the subset of HROM element's DOFs. This ensures that only the relevant DOFs contribute to the projection.

This gives:
$$\Psi^T J_h \Phi q = -\Psi^T R_h$$

or equivalently,
$$(J_{c} \Phi)^T J_h \Phi q = -(J_{c} \Phi)^T R_h$$

Changes in LSPG Builder and Solver:

SetUpDofSet

• Added and overrode SetUpDofSet to introduce the complementary mesh elements.
• Implemented FindNeighbouringElementsAndConditions(rModelPart).

BuildWithComplementaryMeshAndApplyDirichletConditions

• Introduced a method to build the system with the complementary mesh and apply Dirichlet conditions.

InitializeSelectedDofs

• Added a function to populate the mSelectedDofs set with the DOFs that are part of the selected elements and conditions. This set is then used to determine which rows of the system matrix should be zeroed out in subsequent time steps.

ZeroOutUnselectedComplementaryMeshRows

• Introduced a function to zero out the rows of the system matrix 'rA' that correspond to the DOFs of the complementary mesh. This function uses the mSelectedDofs set to determine which rows should remain non-zero.

BuildWithComplementaryMesh

• Introduced a function to perform the build of the LHS and RHS on the selected elements and the corresponding complementary mesh. This function takes into account the integration scheme and the model part of the problem to solve, resulting in the LHS matrix and RHS vector.

Summary of other Changes:

• applications/RomApplication/custom_python/add_custom_utilities_to_python.cpp

  • Exported new functions to Python.

• applications/RomApplication/custom_utilities/rom_auxiliary_utilities.cpp & applications/RomApplication/custom_utilities/rom_auxiliary_utilities.h

  • Introduced a method SetHRomComputingModelPartWithNeighbours to set the HROM model part, including neighboring entities based on nodal weights.
  • Added the GetJPhiElemental function to obtain the JPhi elemental matrix for a particular element.

• applications/RomApplication/custom_utilities/rom_residuals_utility.h

  • Introduced the method GetProjectedResidualsOntoJPhi for obtaining projected residuals.

• applications/RomApplication/python_scripts/hrom_training_utility.py

  • Implemented functionalities for retrieving HROM matrices and projecting residuals onto JPhi.
  • Added routines for preparing and writing the HROM model part, augmented with neighboring elements for LSPG.

• applications/RomApplication/python_scripts/petrov_galerkin_training_utility.py

  • Corrected a minor error: Changed GetRightRomBasis to GetRightROMBasis.

• applications/RomApplication/python_scripts/rom_manager.py

  • Introduced trainHROMLSPG and runHROMLSPG options within the self._ChangeRomFlags method to accommodate HROM LSPG simulations.

Test-related changes:

• applications/RomApplication/tests/fluid_dynamics_test_files/LSPGHROM/ExpectedOutputLSPGHROM.npy
• applications/RomApplication/tests/fluid_dynamics_test_files/LSPGHROM/ProjectParametersHROM.json
• applications/RomApplication/tests/fluid_dynamics_test_files/LSPGHROM/couette_flow_testHROM.mdpa
• applications/RomApplication/tests/fluid_dynamics_test_files/LSPGHROM/rom_data/HROM_ConditionIds.npy
• applications/RomApplication/tests/fluid_dynamics_test_files/LSPGHROM/rom_data/HROM_ConditionWeights.npy
• applications/RomApplication/tests/fluid_dynamics_test_files/LSPGHROM/rom_data/HROM_ElementIds.npy
• applications/RomApplication/tests/fluid_dynamics_test_files/LSPGHROM/rom_data/HROM_ElementWeights.npy
• applications/RomApplication/tests/fluid_dynamics_test_files/LSPGHROM/rom_data/RomParameters.json
• applications/RomApplication/tests/test_fluid_lspg_rom.py

[Rbravo555]

Preliminary review looking good. Just two comments that could well be added as TODOs for future PRs

[RiccardoRossi]

what is missing here?

[Rbravo555]

Let us just catch whether "elemental" or "global" is requested for LSPG, and raise a warning when "elemental" is selected. Only "global" LSPG is implemented