Computational Mathematics and Simulation
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Towing to the massive increase in computing power seen over the past decades, complex numerical simulations have become a key tool both in science and industry. This focus area introduces students to the mathematical and algorithmic foundations underlying numerical simulation. It comprises the rigorous mathematical analysis of numerical methods, often concerned with issues of discretization, approximation and convergence, the development and analysis of numerical algorithms, the implementation of these algorithms on modern computer architectures, and the use of numerical methods in conjunction with mathematical modeling to solve large-scale practical problems. Particular research foci are numerical methods for partial differential equations (finite elements, adaptive finite element methods), numerical linear algebra, PDE-constrained optimization, model order reduction techniques, and algorithms for uncertainty quantification.
The list of elective courses in this specialized area is not limited to the list given below, and the list is expanded on a continuing basis; courses outside the list can be accepted as electives subject to approval by the student's adviser.