Introduction to Partial Differential Equations
Many phenomena in real life applications are modeled by partial differential equations (PDEs). These mathematical models are sets of equations, which describe the essential behavior of a natural or artificial system, in order to forecast and control its evolution. We will give an overview on the derivation of PDEs from physical applications and discuss their mathematical background. The theoretical investigations will be accompanied by the introduction and implementation of numerical schemes for their actual solution with FEniCSX (https://numfocus.org/project/fenics-project), an open-source Finite Element Platform sponsored by NUMFocus (Google).
Knowledge and understanding of the foundations of partial differential equations and finite element methods for their numerical solution in HPC.
Direct instruction plus hands-on exercises.
Project exam (with report and oral presentation)