weighted BFBT Preconditioner

[tjhei]

• merge first matrix-based implementation, Implement BFBT preconditioner #5753
• add tests/benchmarks
• Run a large scaling test
• Add AMG for Schur complement block
• Experiment with skipping inner S solve and switching outer solver to GMRES/IDR
• matrix-free implementation

FYI @quangx

[tjhei]

examples to test:

• coobook/convection_box/
• benchmarks/burstedde/
• benchmarks/annulus

[quangx]

examples to test:

• coobook/convection_box/
• benchmarks/burstedde/
• benchmarks/annulus

Below is a table with iteration counts. Linear solver tolerance is set to 1e-10 for convection box and burstedde and 1e-6 for annulus.

Preconditioner	Convection box	Burstedde	Annulus	Steinberger	Continental extension
Weighted BFBT	53	68	47	div by 0	5000+
Inverse Mass Matrix	50	34	56	-	-

[tjhei]

cookbooks/steinberger?
cookbooks/continental_extension?

[jdannberg]

Some more suggestions:

2D Spherical

2D compressible convection with a reference profile and material properties from BurnMan
coookbooks/burnman/burnman.prm
→ need to set end time to 0

2D spherical, top: fixed velocity, bottom: tangential; T-dependent viscosity + viscosity jumps
→ this one could be used to test different formulations for the mass conservations equation as well (like projected density) if we think that might cause problems

Convection using a pressure–temperature look-up table and the rheology of Steinberger and Calderwood (2006)
cookbooks/steinberger/steinberger.prm
→ need to set end time to 0
2D quarter spherical shell with periodic boundary; projected density approximation, strong viscosity contrasts

Since the one above did not work: could try
Thermochemical plume model using multiple P–T look-up tables
cookbooks/multicomponent_steinberger/steinberger_thermochemical_plume.prm
This is like the one above, but with tangential velocity boundaries on all sides, and without the projected density approximation

3D spherical

benchmarks/nsinker_spherical_shell/gmg.prm
3D spherical, fized velocity top+ bottom

2D box

Sublithospheric convection beneath an oceanic plate with a grain size dependent rheology
cookbooks/grain_size_ridge/grain_size_ridge.prm
→ need to set end time to 0
combination of prescribed velocity and traction boundaries, very strong viscosity contrasts

3D box

relatively simple:
Using the World Builder to model the thermal structure of oceanic transform faults
cookbooks/transform_fault_behn_2007/temperature_dependent.prm (There’s aslo an isoviscous version in the same folder)
→ need to set end time to 0
combination of fixed boundary velocity and traction (material can flow through bottom, left, right boundaries)

[quangx]

Test	Inverse Mass Matrix	Weighted BFBT
2D Spherical	90,82	No convergence
3D Spherical (3,4 levels)	120, No convergence	56 , 82
2D box	-	No convergence
3D box	-	No convergence
Convection box	50	53
Burstedde	34	68
Annulus	56	47
Steinberger	-	Division by 0
Continental extension	-	No convergence

[tjhei]

burnman.prm works when you set the pressure scaling to 1. This likely means something is still off with pressure scaling.