From 34941979b9c376d8275ab37e5f1c9304275c689e Mon Sep 17 00:00:00 2001 From: Jian HUANG Date: Tue, 7 Jul 2026 10:58:16 -0500 Subject: [PATCH 1/8] update publications --- src/docs/sphinx/Publications.rst | 46 ++++++++++++++++++-------------- 1 file changed, 26 insertions(+), 20 deletions(-) diff --git a/src/docs/sphinx/Publications.rst b/src/docs/sphinx/Publications.rst index 9a81c0f20ff..0b5ebfe849b 100644 --- a/src/docs/sphinx/Publications.rst +++ b/src/docs/sphinx/Publications.rst @@ -2,7 +2,7 @@ Publications ############################################################################### -Last updated 10-October-2025 +Last updated 07-July-2026 Referencing GEOS ========================= @@ -24,20 +24,6 @@ Preprints and Early-Views :widths: 100 :header-rows: 0 - * - | **A robust framework for frictional fault contact in geological formations using a stabilized augmented Lagrangian approach** - | M Frigo, N Castelletto, M Cusini, RR Settgast, HA Tchelepi - | arXiv preprint - | `arXiv:2509.20528 `_ - - * - | **Recurrent Transformer U-Net surrogate for flow modeling and data assimilation in subsurface formations with faults** - | Y Han, LJ Durlofsky - | arXiv preprint - | `arXiv:2508.16631 `_ - - * - | **Semi-Analytical Approaches for Addressing Thermal Debonding Issues in Cased Wellbores** - | T Nguyen-Sy, J Huang, H Gross, FP Hamon - | SSRN preprint - | `doi:10.2139/ssrn.5208966 `_ 2026 @@ -52,6 +38,31 @@ Preprints and Early-Views | Computer Methods in Applied Mechanics and Engineering | `doi:10.1016/j.cma.2025.118399 `_ + * - | **A robust framework for frictional fault contact in geological formations using a stabilized augmented Lagrangian approach** + | M Frigo, N Castelletto, M Cusini, RR Settgast, HA Tchelepi + | Journal of Computational Physics + | `doi:10.1016/j.jcp.2026.114988 `_ + + * - | **Recurrent Transformer U-Net surrogate for flow modeling and data assimilation in subsurface formations with faults** + | Y Han, LJ Durlofsky + | Journal of Computational Physics + | `doi:10.1016/j.jcp.2026.114801 `_ + + * - | **Simulation of Multiphase Flow and Poromechanical Effects Around Injection Wells in CO2 Storage Sites** + | J Huang, F Hamon, M Cusini, T Gazzola, RR Settgast, JA White, H Gross + | Rock Mechanics and Rock Engineering + | `doi:10.1007/s00603-024-04051-w `_ + + * - | **High-Resolution Simulations of Geological CO2 Injection: Application to the SPE11 Benchmark** + | D Kachuma, R Hasanzade, P Tomin, ME Thomadakis, J Franc, VAP Magri, TJ Byer, M Cusini, RR Settgast, H Gross, N Castelletto + | SPE Journal + | `doi:10.2118/231182-PA `_ + + * - | **Basin-scale analysis of Mokelumne River Formation for multi-well CO2 injection** + | A Zibitsker, B Schmidt, T Byer, N Castelletto, J Iyer + | International Journal of Greenhouse Gas Control + | `doi:10.1016/j.ijggc.2026.104703 `_ + 2025 ==== @@ -113,11 +124,6 @@ Preprints and Early-Views | Advances in Water Resources | `doi:10.1016/j.advwatres.2024.104678 `_ - * - | **Simulation of Multiphase Flow and Poromechanical Effects Around Injection Wells in CO2 Storage Sites** - | J Huang, F Hamon, M Cusini, T Gazzola, RR Settgast, JA White, H Gross - | Rock Mechanics and Rock Engineering - | `doi:10.1007/s00603-024-04051-w `_ - * - | **Learning CO2 plume migration in faulted reservoirs with Graph Neural Networks** | X Ju, FP Hamon, G Wen, R Kanfar, M Araya-Polo, HA Tchelepi | Computers & Geosciences From 4cddec1d2e564df8eb67f490c11054440e6ec692 Mon Sep 17 00:00:00 2001 From: Jian HUANG Date: Tue, 7 Jul 2026 11:45:14 -0500 Subject: [PATCH 2/8] fix error for doc build --- src/docs/sphinx/Publications.rst | 5 ----- 1 file changed, 5 deletions(-) diff --git a/src/docs/sphinx/Publications.rst b/src/docs/sphinx/Publications.rst index 0b5ebfe849b..baad1ae944f 100644 --- a/src/docs/sphinx/Publications.rst +++ b/src/docs/sphinx/Publications.rst @@ -20,11 +20,6 @@ Referencing GEOS Preprints and Early-Views ========================= -.. list-table:: - :widths: 100 - :header-rows: 0 - - 2026 ==== From 0d6991d2f0c3c3860fa0c7d8243d15eaa08275a0 Mon Sep 17 00:00:00 2001 From: Jian HUANG Date: Tue, 7 Jul 2026 14:32:33 -0500 Subject: [PATCH 3/8] fix the failure for the button-ref directive --- src/index.rst | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/src/index.rst b/src/index.rst index a912239cb52..af4ab52348e 100644 --- a/src/index.rst +++ b/src/index.rst @@ -39,7 +39,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - .. button-ref:: QuickStart + :ref:`QuickStart` :expand: :color: info :click-parent: @@ -55,7 +55,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - .. button-ref:: Tutorials + :ref:`Tutorials` :expand: :color: info :click-parent: @@ -71,7 +71,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - .. button-ref:: BasicExamples + :ref:`BasicExamples` :expand: :color: info :click-parent: @@ -87,7 +87,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - .. button-ref:: AdvancedExamples + :ref:`AdvancedExamples` :expand: :color: info :click-parent: @@ -103,7 +103,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - .. button-ref:: UserGuide + :ref:`UserGuide` :expand: :color: info :click-parent: From ffafbd381ca1e9fe18d4cfa03a127bd5a6b51a16 Mon Sep 17 00:00:00 2001 From: Jian HUANG Date: Tue, 7 Jul 2026 15:42:45 -0500 Subject: [PATCH 4/8] switch to button-link --- src/index.rst | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/src/index.rst b/src/index.rst index af4ab52348e..d633a78175c 100644 --- a/src/index.rst +++ b/src/index.rst @@ -39,7 +39,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - :ref:`QuickStart` + .. button-link:: QuickStart.html :expand: :color: info :click-parent: @@ -55,7 +55,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - :ref:`Tutorials` + .. button-link:: tutorials/Index.html :expand: :color: info :click-parent: @@ -71,7 +71,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - :ref:`BasicExamples` + .. button-link:: basicExamples/Index.html :expand: :color: info :click-parent: @@ -87,7 +87,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - :ref:`AdvancedExamples` + .. button-link:: advancedExamples/Index.html :expand: :color: info :click-parent: @@ -103,7 +103,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - :ref:`UserGuide` + .. button-link:: userGuide/Index.html :expand: :color: info :click-parent: From 009e96f0bfe9d5b39e615e712de46bca6e17a250 Mon Sep 17 00:00:00 2001 From: Jian HUANG Date: Tue, 7 Jul 2026 16:06:47 -0500 Subject: [PATCH 5/8] add path --- src/index.rst | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/src/index.rst b/src/index.rst index d633a78175c..1e52aa22f49 100644 --- a/src/index.rst +++ b/src/index.rst @@ -39,7 +39,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - .. button-link:: QuickStart.html + .. button-link:: docs/sphinx/QuickStart.html :expand: :color: info :click-parent: @@ -55,7 +55,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - .. button-link:: tutorials/Index.html + .. button-link:: docs/sphinx/tutorials/Index.html :expand: :color: info :click-parent: @@ -71,7 +71,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - .. button-link:: basicExamples/Index.html + .. button-link:: docs/sphinx/basicExamples/Index.html :expand: :color: info :click-parent: @@ -87,7 +87,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - .. button-link:: advancedExamples/Index.html + .. button-link:: docs/sphinx/advancedExamples/Index.html :expand: :color: info :click-parent: @@ -103,7 +103,7 @@ you have suggestions for improving the guides below, please post an issue on our +++ - .. button-link:: userGuide/Index.html + .. button-link:: docs/sphinx/userGuide/Index.html :expand: :color: info :click-parent: From 77c5c6208f9a04b134b346e9d8be5c1f5acdf743 Mon Sep 17 00:00:00 2001 From: Jian HUANG Date: Thu, 9 Jul 2026 10:11:39 -0500 Subject: [PATCH 6/8] fix links for reference --- .../validationStudies/carbonStorage/buckleyLeverett/Example.rst | 2 +- .../hydraulicFracture/kgdValidation/Example.rst | 2 +- .../thermoPoromechanics/thermalConsolidation/Example.rst | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/src/docs/sphinx/advancedExamples/validationStudies/carbonStorage/buckleyLeverett/Example.rst b/src/docs/sphinx/advancedExamples/validationStudies/carbonStorage/buckleyLeverett/Example.rst index 9aedba305d5..12705ec12c8 100644 --- a/src/docs/sphinx/advancedExamples/validationStudies/carbonStorage/buckleyLeverett/Example.rst +++ b/src/docs/sphinx/advancedExamples/validationStudies/carbonStorage/buckleyLeverett/Example.rst @@ -9,7 +9,7 @@ **Context** In this example, we simulate a CO2 core flood experiment representing immiscible transport of two-phase -flow (CO2 and water) through porous media `(Ekechukwu et al., 2022) `__. This problem is solved using the multiphase flow solver in GEOS to obtain the temporal evolution of saturation along the flow direction, and verified against the Buckley-Leverett analytical solutions `(Buckley and Leverett, 1942; `__ `Arabzai and Honma, 2013) `__. +flow (CO2 and water) through porous media `(Ekechukwu et al., 2022) `__. This problem is solved using the multiphase flow solver in GEOS to obtain the temporal evolution of saturation along the flow direction, and verified against the Buckley-Leverett analytical solutions `(Buckley and Leverett, 1942; `__ `Arabzai and Honma, 2013) `__. **Input file** diff --git a/src/docs/sphinx/advancedExamples/validationStudies/hydraulicFracture/kgdValidation/Example.rst b/src/docs/sphinx/advancedExamples/validationStudies/hydraulicFracture/kgdValidation/Example.rst index 95d84bb7b4c..29c8ba27eb5 100644 --- a/src/docs/sphinx/advancedExamples/validationStudies/hydraulicFracture/kgdValidation/Example.rst +++ b/src/docs/sphinx/advancedExamples/validationStudies/hydraulicFracture/kgdValidation/Example.rst @@ -8,7 +8,7 @@ Validating KGD Hydraulic Fracture with Experiment **Context** -In this example, we use GEOS to model a planar hydraulic fracture propagating in a finite domain subject to traction-free external boundaries. Contrary to the classic KGD problems, we do not assume an infinite rock domain. Existing analytical solutions cannot model fracture behavior in this scenario, so this problem is solved using the hydrofracture solver in GEOS. We validate the simulation results against a benchmark experiment `(Rubin, 1983) `__. +In this example, we use GEOS to model a planar hydraulic fracture propagating in a finite domain subject to traction-free external boundaries. Contrary to the classic KGD problems, we do not assume an infinite rock domain. Existing analytical solutions cannot model fracture behavior in this scenario, so this problem is solved using the hydrofracture solver in GEOS. We validate the simulation results against a benchmark experiment `(Rubin, 1983) `__. **Input file** diff --git a/src/docs/sphinx/advancedExamples/validationStudies/thermoPoromechanics/thermalConsolidation/Example.rst b/src/docs/sphinx/advancedExamples/validationStudies/thermoPoromechanics/thermalConsolidation/Example.rst index 07922a086b9..32461b48560 100644 --- a/src/docs/sphinx/advancedExamples/validationStudies/thermoPoromechanics/thermalConsolidation/Example.rst +++ b/src/docs/sphinx/advancedExamples/validationStudies/thermoPoromechanics/thermalConsolidation/Example.rst @@ -8,7 +8,7 @@ Thermoporoelastic Consolidation **Context** Thermoporoelastic consolidation is a typical fully coupled problem which involves solid deformation, fluid flow and heat transfer in saturated porous media. -In this example, we use the GEOS coupled solvers to solve a one-dimensional thermoporoelastic consolidation problem with a non-isothermal boundary condition, and we verify the accuracy of the results using the analytical solution provided in `(Bai, 2005) `__ +In this example, we use the GEOS coupled solvers to solve a one-dimensional thermoporoelastic consolidation problem with a non-isothermal boundary condition, and we verify the accuracy of the results using the analytical solution provided in `(Bai, 2005) `__ **InputFile** From 6f8d8b12e99bb6fa037e780c6417c2d04aef3e91 Mon Sep 17 00:00:00 2001 From: DENEL Bertrand Date: Thu, 9 Jul 2026 13:43:51 -0500 Subject: [PATCH 7/8] Fixed hyperlinks --- src/coreComponents/fileIO/doc/InputXMLFiles.rst | 2 +- src/coreComponents/fileIO/doc/OutputTasks.rst | 2 +- src/coreComponents/linearAlgebra/docs/LinearSolvers.rst | 2 +- .../mesh/mpiCommunications/docs/SpatialPartition.rst | 4 ++-- .../contact/docs/SolidMechanicsEmbeddedFractures.rst | 4 ++-- src/docs/sphinx/buildGuide/ContinuousIntegration.rst | 4 +--- src/docs/sphinx/buildGuide/Dependencies.rst | 4 ++-- src/docs/sphinx/tutorials/step01/Tutorial.rst | 2 +- 8 files changed, 11 insertions(+), 13 deletions(-) diff --git a/src/coreComponents/fileIO/doc/InputXMLFiles.rst b/src/coreComponents/fileIO/doc/InputXMLFiles.rst index 15fb463ca82..fb1b66ab32c 100644 --- a/src/coreComponents/fileIO/doc/InputXMLFiles.rst +++ b/src/coreComponents/fileIO/doc/InputXMLFiles.rst @@ -266,7 +266,7 @@ Advanced XML Features ================================= The `geosx_xml_tools` python package adds a set of advanced features to the GEOS xml format: units, parameters, and symbolic expressions. -See`Python Tools Setup `_ for details on setup instructions, and `XML Parser Documentation `_ for package API details. +See `Python Tools Setup `_ for details on setup instructions, and `XML Parser Documentation `_ for package API details. Usage diff --git a/src/coreComponents/fileIO/doc/OutputTasks.rst b/src/coreComponents/fileIO/doc/OutputTasks.rst index b8d91d92fed..9d79f9440bc 100644 --- a/src/coreComponents/fileIO/doc/OutputTasks.rst +++ b/src/coreComponents/fileIO/doc/OutputTasks.rst @@ -195,7 +195,7 @@ time history datat. .. _SILO: https://wci.llnl.gov/simulation/computer-codes/silo .. _VTK: https://vtk.org/wp-content/uploads/2015/04/file-formats.pdf -.. _HDF5: https://portal.hdfgroup.org/display/HDF5/HDF5 +.. _HDF5: https://www.hdfgroup.org/solutions/hdf5 .. _VisIT: https://wci.llnl.gov/simulation/computer-codes/visit/downloads .. _Paraview: https://www.paraview.org/ .. _MatPlotLib: https://matplotlib.org/ diff --git a/src/coreComponents/linearAlgebra/docs/LinearSolvers.rst b/src/coreComponents/linearAlgebra/docs/LinearSolvers.rst index e7390348681..a6e816ba6d7 100644 --- a/src/coreComponents/linearAlgebra/docs/LinearSolvers.rst +++ b/src/coreComponents/linearAlgebra/docs/LinearSolvers.rst @@ -305,7 +305,7 @@ This section provides a brief description of the available preconditioners. * **ILUK**: incomplete LU factorization with fill level k of the original matrix: :math:`\mathsf{M}^{-1} = \mathsf{U}^{-1} \mathsf{L}^{-1}`. Further details can be found in: - - `HYPRE documentation `__, + - `HYPRE documentation `__, - `PETSc documentation `__, - `Trilinos documentation `__. diff --git a/src/coreComponents/mesh/mpiCommunications/docs/SpatialPartition.rst b/src/coreComponents/mesh/mpiCommunications/docs/SpatialPartition.rst index ca141be0514..0c8a7567f81 100644 --- a/src/coreComponents/mesh/mpiCommunications/docs/SpatialPartition.rst +++ b/src/coreComponents/mesh/mpiCommunications/docs/SpatialPartition.rst @@ -81,6 +81,6 @@ Therefore, it is a good practice or habit to hide ghost objects using ghostRank If the visualization method involves interpolation, such as interpolating a zonal field into a nodal field or generating contours, the interpretation near partition boundaries is not accurate. -.. _METIS: http://glaros.dtc.umn.edu/gkhome/metis/metis/overview -.. _PARMETIS: http://glaros.dtc.umn.edu/gkhome/metis/parmetis/overview +.. _METIS: https://github.com/KarypisLab/METIS +.. _PARMETIS: https://github.com/KarypisLab/ParMETIS .. _PTSCOTCH: https://www.labri.fr/perso/pelegrin/scotch/ \ No newline at end of file diff --git a/src/coreComponents/physicsSolvers/solidMechanics/contact/docs/SolidMechanicsEmbeddedFractures.rst b/src/coreComponents/physicsSolvers/solidMechanics/contact/docs/SolidMechanicsEmbeddedFractures.rst index 5cf3a8ce3f9..5d39212805a 100644 --- a/src/coreComponents/physicsSolvers/solidMechanics/contact/docs/SolidMechanicsEmbeddedFractures.rst +++ b/src/coreComponents/physicsSolvers/solidMechanics/contact/docs/SolidMechanicsEmbeddedFractures.rst @@ -43,9 +43,9 @@ The following data are allocated and used by the solver: References ========== -1. Simo JC, Rifai MS. A class of mixed assumed strain methods and the method of incompatible modes. *Int J Numer Methods Eng.* 1990;29(8):1595-1638. Available at: http://arxiv.org/abs/https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.1620290802. +1. Simo JC, Rifai MS. A class of mixed assumed strain methods and the method of incompatible modes. *Int J Numer Methods Eng.* 1990;29(8):1595-1638. Available at: https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.1620290802. -2. Foster CD, Borja RI, Regueiro RA. Embedded strong discontinuity finite elements for fractured geomaterials with variable friction. *Int J Numer Methods Eng.* 2007;72(5):549-581. Available at: http://arxiv.org/abs/https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.2020. +2. Foster CD, Borja RI, Regueiro RA. Embedded strong discontinuity finite elements for fractured geomaterials with variable friction. *Int J Numer Methods Eng.* 2007;72(5):549-581. Available at: https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.2020. 3. Wells G, Sluys L. Three-dimensional embedded discontinuity model for brittle fracture. *Int J Solids Struct.* 2001;38(5):897-913. Available at: https://doi.org/10.1016/S0020-7683(00)00029-9. diff --git a/src/docs/sphinx/buildGuide/ContinuousIntegration.rst b/src/docs/sphinx/buildGuide/ContinuousIntegration.rst index 3740fe464a3..402c3c7ea11 100644 --- a/src/docs/sphinx/buildGuide/ContinuousIntegration.rst +++ b/src/docs/sphinx/buildGuide/ContinuousIntegration.rst @@ -6,9 +6,7 @@ Continuous Integration process To save building time, the third party libraries (that do not change so often) and GEOS are build separately. Everytime a pull is requested in the TPL repository, docker images are generated and deployed on `dockerhub `_. -The repository names (`ubuntu18.04-gcc8 `_, -`centos7.7.1908-clang9.0.0 `_, `centos7.6.1810-gcc8.3.1-cuda10.1.243 `_ etc.) -obviously reflect the OS and the compiler flavour used. +The repository names (e.g. `ubuntu24.04-gcc13-cuda12.9.1 `_) obviously reflect the OS and the compiler flavour used. For each image, the unique tag ``${PULL_REQUEST_NUMBER}-${BUILD_NUMBER}`` (defined as ``${{ github.event.number }}-${{ github.run_number }}`` in github actions) is used so we can connect the related code source in a rather convenient way. Each docker contains the ``org.opencontainers.image.created`` and ``org.opencontainers.image.revision`` labels to provide additional information. diff --git a/src/docs/sphinx/buildGuide/Dependencies.rst b/src/docs/sphinx/buildGuide/Dependencies.rst index 03824bb29a4..1ac14328374 100644 --- a/src/docs/sphinx/buildGuide/Dependencies.rst +++ b/src/docs/sphinx/buildGuide/Dependencies.rst @@ -57,10 +57,10 @@ uncrustify_ 401a409 :code:`ENABLE_UNCRUSTIFY` :code:`UNCRUSTIFY_EXECUTABL .. _conduit: https://github.com/LLNL/conduit .. _CHAI : https://github.com/LLNL/CHAI .. _RAJA : https://github.com/LLNL/RAJA -.. _hdf5 : https://portal.hdfgroup.org/display/HDF5/HDF5 +.. _hdf5 : https://www.hdfgroup.org/solutions/hdf5 .. _mathpresso : https://github.com/kobalicek/mathpresso .. _pugixml : https://pugixml.org -.. _parmetis : http://glaros.dtc.umn.edu/gkhome/metis/parmetis/overview +.. _parmetis : https://github.com/KarypisLab/ParMETIS .. _silo : https://wci.llnl.gov/simulation/computer-codes/silo .. _VTK : https://vtk.org/ .. _suitesparse : https://people.engr.tamu.edu/davis/suitesparse.html diff --git a/src/docs/sphinx/tutorials/step01/Tutorial.rst b/src/docs/sphinx/tutorials/step01/Tutorial.rst index 8c9b5697689..e67d33b3788 100644 --- a/src/docs/sphinx/tutorials/step01/Tutorial.rst +++ b/src/docs/sphinx/tutorials/step01/Tutorial.rst @@ -137,7 +137,7 @@ In production runs, you may want to suppress most console output. For solvers of the ``SinglePhaseFVM`` family, one required attribute is a discretization scheme. Here, we use a Two-Point Flux Approximation (TPFA) finite volume discretization scheme called ``singlePhaseTPFA``. -To know the list of admissible values of an attribute, please see `GEOS's XML schema `_. +To know the list of admissible values of an attribute, please see `GEOS's XML schema `_. This discretization type must know how to find permeability values that it uses internally to compute transmissibilities. The ``permeabilityNames`` attribute tells the solver the user-defined name (the *handle*) of the permeability values that will be defined elsewhere in the input file. From 2cda25c62ebd7712c667265dc6a01b7bd3b33613 Mon Sep 17 00:00:00 2001 From: Jian HUANG Date: Thu, 9 Jul 2026 16:53:56 -0500 Subject: [PATCH 8/8] address review comment --- src/coreComponents/linearAlgebra/docs/LinearSolvers.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/coreComponents/linearAlgebra/docs/LinearSolvers.rst b/src/coreComponents/linearAlgebra/docs/LinearSolvers.rst index a6e816ba6d7..9e690b8abf3 100644 --- a/src/coreComponents/linearAlgebra/docs/LinearSolvers.rst +++ b/src/coreComponents/linearAlgebra/docs/LinearSolvers.rst @@ -312,7 +312,7 @@ This section provides a brief description of the available preconditioners. * **ILUT**: a dual threshold incomplete LU factorization: :math:`\mathsf{M}^{-1} = \mathsf{U}^{-1} \mathsf{L}^{-1}`. Further details can be found in: - - `HYPRE documentation `__, + - `HYPRE documentation `__, - not yet available through PETSc interface, - `Trilinos documentation `__.