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The course focuses on crucial aspects for Scientific Computing, providing an overview of the steps required to address numerical simulations of mathematical and physical problems, from the selection of optimal strategies to applications. Moreover, it covers specific advanced tools, involving both numerical and modeling aspects (such as, e.g., the so-called phase-field model), which proved useful for addressing state-of-the-art problems in applied scientific computing.
The major aspects covered by lectures are:
i) Numerical methods for solving ODEs and PDEs (focus on Finite Difference and Spectral Methods);
ii) Diffuse Interface Approaches (e.g., phase-field methods) and other convenient approaches for solving specific classes of equations/problems (e.g., Monte Carlo methods)
iii) Implementing methods and numerical schemes, testing algorithm, comparing performances
iv) Basics of programming in Python to perform computations/simulations
Exercises will be assigned periodically to apply the concept discussed during the lectures, and develop practical skills, allowing students to exploit scientific computing further in their career. Their solution will be provided and discussed during lectures as well.
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