Combining adaptive mesh refinement with a parallel multilevel BDDC solver

This research was supported by the Czech Science Foundation through grant 1809628S, and by the Czech Academy of Sciences through RVO:67985840. Computational time on the Salomon supercomputer has been provided by the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070), funded by the European Regional Development Fund and the national budget of the Czech Republic via the Research and Development for Innovations Operational Programme, as well as Czech Ministry of Education, Youth and Sports via the project Large Research, Development and Innovations Infrastructures (LM2011033).Adaptive mesh refinement and domain decomposition. Adaptive mesh refinement is an important part of solving problems with complicated solutions or when a prescribed accuracy needs to be achieved. In this approach, solution is found on a given mesh and its local error is estimated. Regions where the estimated error is high are then refined to improve the accuracy, and the solution is recomputed. This strategy leads to accumulation of degrees of freedom to regions with abrupt changes in the solution, such as boundary or internal layers