This course gives a broad introduction to numerical algorithms used in scientific computing. It covers classical methods to solve Ordinary and Partial Differential Equations such as spectral, finite difference and finite volume methods. A brief introduction to finite element methods is given. Explicit and implicit time integration using various high-order methods are discussed. We review basic methods to solve linear and non-linear systems of equations. Issues related to the implementation of efficient algorithms on modern high-performance computing systems are discussed. Hyperbolic systems of conservations laws are covered in detail.

Analysis of methods for the numerical solution of the partial differential equations of plasma physics, including those of elliptic, parabolic, hyperbolic, and eigenvalue type. Topics include finite difference, finite element, spectral, particle-in-cell, Monte Carlo, moving grid, and multiple-time-scale techniques, applied to the problems of plasma equilibrium, transport and stability. Basic parallel programming concepts are discussed.

This course examines methods for simulating matter at the atomistic scale with emphasis on the concepts that underline modern computational methodologies for classical many-body systems at or near statistical equilibrium. The course covers Monte Carlo and Molecular Dynamics (from basics to advanced techniques), and includes an introduction to ab-initio Molecular Dynamics and the use of Machine Learning techniques in molecular simulations.Central to the learning experience will be a set of self-contained numerical projects on simple model systems, using popular simulation packages to provide hands-on experience on the matter of the course.