EU Regional School - Maday Seminar
Prof. Yvon Maday - The Reduced Basis Element Method: Application to Fluid Flow and Maxwell's Equations
Université Pierre et Marie Curie, Paris
Reduced basis methods are particularly attractive to use in order to diminish the number of degrees of freedom associated with the approximation of a set of partial differential equations. The main idea is to construct ad hoc basis functions with a large information content. In this talk, we present reduced basis methods for simulating problems in fluid flow and for the time-harmonic Maxwell's equations. We decompose the geometry into generic parts, and to construct a reduced basis for these generic parts by considering representative geometric snapshots. The global system is constructed by appropriately "gluing" the individual basis solutions together through Lagrange multipliers or "automatically" through the choice of discretization.