Mathematical Sciences: Topics in Applied Mathematics

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This project involves research in the areas of applied mathematics related to petroleum engineering and geophysics. The petroleum engineering work will consider simulation of flows in porous media, including, in particular, multiphase flow in naturally fractured petroleum reservoirs. Attenuated waves are best described by means of hyperbolic pseudo-differential equations. Much of the research will be devoted to developing numerical methods for such waves, with emphasis on attenuated waves in porous media saturated by single- or multiphase fluids; interpretation of scattering phenomena related to the slow compression wave in Biot media will be studied by means of homogenization theory. Applications of the same concepts in elasticity theory and electromagnetic theory will be considered. Several numerical analysis questions related to these problems will be treated. This research will have applications in structural analysis and electromagnetic theory.