Added docs for HMG

framework/doc/content/source/preconditioners/HMGPreconditioner.md

@@ -0,0 +1,65 @@
+# HMG (High-performance (Hybrid) multigrid method)
+
+## Overview
+
+[HMG](https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCHMG.html) 's
+essential idea is to separate a multigrid method into two steps;
+matrix coarsening and level solvers. The main motivation of HMG in
+the first place is to use
+[HYPRE](https://computing.llnl.gov/projects/hypre-scalable-linear-solvers-multigrid-methods)
+to do matrix coarsening and generate interpolations
+and use [PETSc](https://www.mcs.anl.gov/petsc/) preconditioners/solvers as level solvers.
+However, the code is more general, and it can use other
+codes such as [GAMG](https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCGAMG.html)
+or a user code to generate interpolations.
+
+
+## Example 1
+
+```
+[Executioner]
+  type = Steady
+
+  solve_type = 'PJFNK'
+
+  petsc_options_iname = '-pc_type'
+  petsc_options_value = 'hmg'
+[]
+```
+
+This configuration use HYPRE to generate interpolations
+and use SOR preconditioners from PETSc as level solvers.
+
+## Example 2
+
+```
+[Executioner]
+  type = Steady
+
+  solve_type = 'PJFNK'
+
+  petsc_options_iname = '-pc_type -pc_hmg_use_subspace_coarsening'
+  petsc_options_value = 'hmg true'
+  petsc_options = '-snes_view'
+[]
+```
+
+If there are multiple nonlinear variables, this configuration will reuse interpolations
+generated for the first nonlinear variable for all other variables. This will significantly
+speedup preconditioner setup.  We demonstrate this capability for
+neutron transport calculations in the following paper:
+
+```tex
+@article{kong2020highly,
+  title={{A Highly Parallel Multilevel Newton--Krylov--Schwarz Method with Subspace-Based Coarsening and Partition-Based Balancing for the Multigroup Neutron Transport Equation on Three-Dimensional Unstructured Meshes}},
+  author={Kong, Fande and Wang, Yaqi and Gaston, Derek R and Permann, Cody J and Slaughter, Andrew E and Lindsay, Alexander D and DeHart, Mark D and Martineau, Richard C},
+  journal={SIAM Journal on Scientific Computing},
+  volume={42},
+  number={5},
+  pages={C193--C220},
+  year={2020},
+  publisher={SIAM}
+}
+```
+
+A complete toy example is [test/tests/preconditioners/hmg/diffusion_hmg.i]

test/tests/preconditioners/hmg/tests

@@ -1,5 +1,5 @@
 [Tests]
-  design = 'Preconditioning/index.md'
+  design = 'HMGPreconditioner.md'
   issues = '#16210'
 
   [hmg]