Integral Operators And Fast Solvers: A Cross-disciplinary Excursus On The Best Of Fft’s Companions

 

Prof. F. P, Andriulli Politecnico di Torino Course Type Type B Calendar 23-27/3/2026 Room Program The discovery of the Fast Fourier Transform (FFT), the fast algorithm to compute the Discrete Fourier Transform, can rightly be considered as one of the most technology-enabling milestones in computational science. The FFT reduces the computational complexity of Fourier analysis from quadratic to (quasi) linear-in-the-length-of-the-signal and it has profoundly impacted several disciplines both in applied science and engineering. One could wonder whether the existence of the FFT is a fortunate, but isolate case or if other technology-enabling “transforms” exist that allow fast algorithms. This course will answer to this question and will take the audience into an exciting journey through the most powerful fast schemes and their stunning multidisciplinary applications. After the introduction of some fundamental and powerful tools from Computational Science & Engineering, the course will present the most relevant and impacting fast algorithms emerging from various disciplines of engineering and applied science. Then the course will focus on a cross-disciplinary selection of applications including models in electric neuroimaging, gravitation, electromagnetics, and applied solid state physics.