Kursy Interdyscyplinarnych Studiów Doktoranckich

Course description: This interdisciplinary course provides an introduction to computational techniques for the simulation of a broad range of engineering and physical systems.  Concepts and methods discussed are widely illustrated by applications drawn from electrical, mechanical, and chemical engineering. Topics include: mathematical formulations of simulation problems; sparse direct and iterative linear system solution techniques, including Krylov subspace methods; preconditioning techniques; Newton methods for nonlinear problems; techniques for ordinary differential equations; stability and convergence for multistep integration methods;  automatic model order reduction techniques for linear dynamical systems.

Course description: This course focuses on modern numerical techniques for linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations (PDEs), and integral equations fundamental to a large variety of applications in science and engineering. Topics include: formulations of problems in terms of initial and boundary value problems; finite difference and finite element discretizations; boundary element approach; fast solution methods for partial differential and integral equations, including Krylov subspace and multipole methods.