The project is concerned with the development of high performance solution methods for large scale structural mechanics problems arising in Geomechanics. The efficient solution of such problems arising from civil engineering, mining, storage of the radioactive waste etc., requires knowledge of the geological structures (sometimes situated far beneath the geosurface), the behaviour of the geomaterials (often nonlinear) and knowledge of the stress-strain state in the investigated domain. Here, the mathematical modelling and computer simulations play an indispensable role as a general (and very often the only available) way for evaluation of the stress-strain state.
The physical phenomena in Geomechanics are described by differential equations leading typically to three-dimensional, complex and large scale mathematical models. When resolving these models one easily comes to a number of degrees of freedom in the range of tens to hundreds of millions, which alone goes beyond the capabilities of many existing commercially available codes and requires the use of supercomputer resources. The successful treatment of the above problems requires the joint knowledge of experts in mathematical modelling, numerical methods and in designing of highly efficient parallel algorithms. Profound experience in such a highly interdisciplinary collaboration has been gained within a Copernicus project, successfully carried out by the same research team.
The major objective of this project is to develop high performance and robust numerical solution methods (including their implementation on contemporary parallel computer systems) applicable to a broad class of problems in Geosciences, related to environmental protection (dimensioning and stability of nuclear waste repository), new technologies in mining, cost-efficiency and reliability of transport constructions (bridges and tunnels).
The mathematical models will be based on the differential equations governing the elastic and elasto-plastic material behaviour. The numerical methods will involve adaptive local refinement and composite grids techniques, combined with suitable a posteriori error estimators. Some non-conforming, mixed or reduced integration finite element methods will be tested to improve the robustness of the discretization. The arising linear systems will be solved by efficient iterative methods based on incomplete factorizations or optimal order algebraic multilevel preconditioning techniques with the emphasis on the parallelization of the preconditioners. Inexact Newton type solvers will be used for the nonlinear systems. All methods will be tested on benchmark problems which represent real-life engineering practice problems.
The project aims require regular contacts and cooperation between the research teams collaborating already during a previous Copernicus project. The accumulated experience will be now a starting point for further tuning the existing methods and implementations, as well as for developing new methods. The cooperation will take place in the form of joint research, mutual visits and workshops. Experience in coordination and management of international research projects is present among the general coordinator. The logistics will be further improved via a scientific coordinator from one of the CCE partner groups. The results will be promoted to the scientific society and to possible industrial users at international conferences and by other means.