PERIOD: MAY - JUNE 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. Theory will be balanced with hands-on computational activities. Prerequisites are limited to standard real analysis and basic programming skills (in any language). Final grades will be based on class participation and on the oral presentation of a final report.

Introductory concepts in Computational Science and Computational Engineering The Discrete Fourier Transform and the FFT Butterfly Algorithm Discretization methods for linear operators An hands-on introduction to LAPACK and other computational libraries An excursus on relevant integral operators and transforms The Fast Gauss Transform Static and dynamic Fast Multipole Methods H-Matrix Algebras and Kernel Free Fast Methods Analysis of selected applications from Computational Neuroimaging, Computational Astrophysics, Computational Electromagnetics, Computational Thermodynamics, and Computational Solid State Physics.

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Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.