MG4HDG-P0

Numerical experiments code of multigrid (MG) preconditioners for condensd lowest-order HDG schemes with projected jumps (HDG-P0) for the reaction-diffusion equations and the generalized Stokes equations

Link to the paper: https://arxiv.org/abs/2208.14418

Requirements:

• Netgen/NGSolve: version: 6.2.2105-289-g53df468f0, website: ngsolve.org.

Files:

• prol: NGSolve add on for intergrid transfer of hybrid facet space, needs to be built and installed.
• mymg.py: Multigrid method class.
• myIterSolver.py: Iteration solver class.
• diff-quad-rate.py: Solve HDG-P0 for reaction-diffusion equations with known solution.
• diff-jump.py: Solve HDG-P0 for reaction-diffusion equations with jump coefficients on the coarsest mesh.
• diff-chess.py: Solve HDG-P0 for reaction-diffusion equations with jump coefficients on the finest mesh in 2D.
• stokes-quad-rate.py: Solve HDG-P0 for the generalized Stokes equations with known solution.
• stokes-lid.py: One-time augmented Lagrangian Uzawa iteration to solve the lid-driven cavity problems.
• stokes-back.py: One-time augmented Lagrangian Uzawa iteration to solve the backward-facing step flow problem.