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geodynamics / aspect

A parallel, extensible finite element code to simulate convection in both 2D and 3D models.
https://aspect.geodynamics.org/
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GMG and Newton solver #3656

Open tjhei opened 4 years ago

tjhei commented 4 years ago

We should implement the Newton terms for the GMG formulation.

@MFraters can you post a formula for the matrix terms that need to be added?

MFraters commented 4 years ago

So I think the equation you are looking in paper https://doi.org/10.1093/gji/ggz183, section 2.3, equation 14, 15 and 16, where J^{uu} is replaced by the equation in the top of section 2.5, where H is replaced by H^{spd} (H == H^{spd} when alpha=1.

tjhei commented 3 years ago

https://github.com/geodynamics/aspect/blob/ea1c999bf29823752efd4c594a9d6fbbe9d8e174/source/simulator/assemblers/newton_stokes.cc#L428-L431

tjhei commented 3 years ago

I think we need to store

Table<2,VectorizedArray<SymmetricTensor<2>>> strain_rate;
Table<2,VectorizedArray<double>> viscosity_derivative_wrt_strain_rate; // * derivative_scaling_factor * alpha
Table<2,VectorizedArray<double>> viscosity_derivative_wrt_pressure; // * derivative_scaling_factor

and the same on each level (basically a MGLevelObject< ....> each)