The paper that describes the tpsa discretization has an inaccuracy related to Robin boundary conditions with anisotropic Robin coefficients: In Equation A2.12 in that paper, it is assumed that the product d c_1 d is equivalent to c_1 d d, however, this does not hold if c_1 is a proper matrix. The same applies to the other relations described on the same line of the paper.
When done properly, without the false commutation of factors in the product, this will result to a slightly more complex discretization scheme. It should also remove an issue noted in the discretization related to the treatment of boundary terms for the solid pressure, where it was noted that anisotropic Robin conditions were not really well described in the model.
Though the paper describes Dirichlet and Neumann conditions as limiting cases of the Robin parameter, I am quite confident that these conditions are correctly implemented. This should of course be verified.
Note for implementation: The natural test case is the shearing of a 3d cube, for which we already have tests implemented with Dirichlet and Neumann conditions (see test_tpsa.py), now also implemented with Robin conditions.
This issue should initially be considered a notification on the problem. We will hopefully get around to address the issue in due course, but this will not be prioritized for the moment.
The paper that describes the tpsa discretization has an inaccuracy related to Robin boundary conditions with anisotropic Robin coefficients: In Equation A2.12 in that paper, it is assumed that the product
d c_1 dis equivalent toc_1 d d, however, this does not hold ifc_1is a proper matrix. The same applies to the other relations described on the same line of the paper.When done properly, without the false commutation of factors in the product, this will result to a slightly more complex discretization scheme. It should also remove an issue noted in the discretization related to the treatment of boundary terms for the solid pressure, where it was noted that anisotropic Robin conditions were not really well described in the model.
Though the paper describes Dirichlet and Neumann conditions as limiting cases of the Robin parameter, I am quite confident that these conditions are correctly implemented. This should of course be verified.
Note for implementation: The natural test case is the shearing of a 3d cube, for which we already have tests implemented with Dirichlet and Neumann conditions (see test_tpsa.py), now also implemented with Robin conditions.
This issue should initially be considered a notification on the problem. We will hopefully get around to address the issue in due course, but this will not be prioritized for the moment.