The TwoScale library#
This is a presentation of the distributed two-scale method introduced in Salzman and Moës [SMoes23] from the seminal work of Duarte et al. [DKBabuvska07] and adapted for use with FEniCSx/PETSc.
The method part gives some hints on the theoretical basis (Theoretical concept), how the method can be used with the FEniCSx/PETSc libraries (Plug the method in FEniCSx : standard workflow with FEniCSx 0.9) and in Dirichlet BC in TwoScale method, an explanation of how Dirichlet boundary conditions are set at the coarse scale.
In Tutorials part some examples of problems solved with the two-scale method are given as notebooks to become familiar with the implemented library. Some are step-by-step example.
Finally, in the API part, you will find Python and C++ documentation of the TwoScale library.
C. A. Duarte, Dae-Jin Kim, and Ivo Babuška. A global-local approach for the construction of enrichment functions for the generalized fem and its application to three-dimensional cracks. In V. M. A. Leitão, C. J. S. Alves, and C. Armando Duarte, editors, Advances in Meshfree Techniques, 1–26. Dordrecht, 2007. Springer Netherlands.
Alexis Salzman and Nicolas Moës. A two-scale solver for linear elasticity problems in the context of parallel message passing. Computer Methods in Applied Mechanics and Engineering, 407:115914, 2023. URL: https://www.sciencedirect.com/science/article/pii/S0045782523000373, doi:https://doi.org/10.1016/j.cma.2023.115914.