The world's ever-growing rate of energy consumption urges the improvement of techniques of both fossil fuels and renewable energy. Hydraulic fracturing is a technique applied to both categories of energy sources. It consists in pumping water at a very high pressure through pre-drilled wells into the ground and generating fractures in the rock. It can be employed to extract crude oil or natural gas from the rock; it can also facilitate the extraction of heat from the earth by forming a network of underground fractures. Its application requires the design of the fracturing strategy, including the quantity and pressure of the water to be injected.Hydraulic fracturing is expensive to study both on site and in a laboratory and only limited information can be obtained wherefrom. On the contrary, computer simulations are cost-effective and time-efficient in predicting the geometry of the fractures and thus can contribute to speeding the designing process. Nevertheless, most state-of-the-art simulation methods for the fracturing process apply only to a (layerwise) homogeneous rock medium.In this project, I plan to develop efficient simulation methods with the objective of accurately predicting the three-dimensional network of hydraulic fractures, taking into account rock self-contact, inhomogeneity, and poroelasticity. I also plan to build methodologies to incorporate stratigraphic data obtained from field technologies. A technical contribution to the field of numerical analysis will be the use of variational inequalities to incorporate the inequality constraints arising in the formulation of the coupled problem between the fluid and the rock medium.I completed my doctoral study and postdoctoral training at Stanford University, United States. In April 2011, I started a four-year tenure-track Assistant Professor position in the Universitat Politecnica de Catalunya, Spain. This grant would provide me a unique opportunity to establish my research career in Europe.