Geometric Multigrid#

ASPECT can optionally use a Geometric Multigrid Solver (GMG) for the efficient solution of the Stokes system (velocity and pressure). When used correctly, this can reduce the compute time spent in the solver by about a factor of 3, and decrease the memory requirements by a factor of 10. For more details about the method see Clevenger and Heister [2021], Clevenger et al. [2020].

To take advantage of the GMG solver, you need to:

Enable it in your parameter file, namely:
```
subsection Solver parameters
  subsection Stokes solver parameters
    set Stokes solver type = block GMG
  end
end
```
See Subsection: Solver parameters / Stokes solver parameters for other parameters that influence the solver behavior.
The GMG solver requires that the viscosity is averaged, either as a constant (for example by using harmonic averaging) or as a \(Q_1\) averaging. (See Averaging material properties for more about averaging.) Averaging other properties is optional. You can use
```
subsection Material model
  set Material averaging = harmonic average
end
```
for example. Note that \(Q_1\) averaging is a bit slower than averaging to a constant per cell, but it might provide more accurate solutions.
Run in release mode. The GMG solver depends on running optimized code, so using optimized mode is more important than for other parts of ASPECT to get good performance. (Of course, the GMG solver also runs in debug mode, and you should do so while setting up a model. You will just not get the same speedup from the non-GMG to the GMG solver in debug mode as you get in release mode.)
Enable vectorization optimizations. The GMG solver takes advantage of special instructions (AVX2, AVX512) in modern CPUs and requires these do be enabled when compiling deal.II. This can be achieved by passing the compiler flag CMAKE_CXX_FLAGS="-march=native" to CMake or setting NATIVE_OPTIMIZATIONS=true in candi.cfg when using candi (see Installation for more information). When you have vectorization enabled, ASPECT will report something like this:

-----------------------------------------------------------------------------
-- This is ASPECT, the Advanced Solver for Problems in Earth's ConvecTion.
--     . version 2.3.0-pre
--     . using deal.II 9.2.0
--     .       with 64 bit indices and vectorization level 3 (512 bits)
--     . using Trilinos 12.10.1
--     . using p4est 2.2.0
--     . running in OPTIMIZED mode
--     . running with 114688 MPI processes
-----------------------------------------------------------------------------
Vectorization over 8 doubles = 512 bits (AVX512), VECTORIZATION_LEVEL=3

Without optimizations enabled, the output will be “and vectorization level 1 (128 bits)” in the fourth line above.