Efficient discretizations and fast solvers for poroelasticity

Poroelasticity, the modeling of coupled mechanics and flow in porous media, has become of increasing importance in a diverse range of engineering fields. Notable applications of poroelasticity can be found in environmental engineering (groundwater/soil contamination), petroleum engineering, hydraulic/thermal fracturing, reservoir engineering (carbon dioxide storage in geological structures) as well as in mechanical engineering (vibro-acoustics and material inspection by ultrasonic). Mathematical models for poroelasticity are based on coupled partial differential equations, which are very challenging to be solved. In this project we will design and analyze new iterative splitting methods for poroelasticity. Higher - order continuous/discontinuous Galerkin methods for the time discretization will be combined with Galerkin finite elements (mechanics) and mixed finite elements (flow). A monolithic solver will be also proposed as alternative to the iterative schemes. This two options will be thoroughly compared. An accurate and fast solver for poroelasticity, implemented in an open source software (deal.II) will be developed.