teaching

Physical phenomena are often described in terms of ordinary and partial differential equations (ODEs and PDEs) with interactions and features on multiple scales. Some of these systems are notoriously hard to solve but are of great interest in scientific and engineering applications. In this course you will learn about state-of-the-art methods and software for the fast numerical solution of such systems, focusing on several types of oscillatory ODEs and PDEs in complex geometric settings. We will cover hybrid methods for oscillatory and stiff ODEs, asymptotic approximations, specialized quadrature methods for numerical integration, and introduce powerful boundary integral-based methods for PDEs. We will review famous publications and use both long-standing and cutting edge software packages.

Physical phenomena are described in terms of ordinary and partial differential equations (ODEs and PDEs). Most of these systems cannot be solved on paper (i.e. do not possess an analytic solution), so we have to resort to numerical methods to find a solution. In this course you will learn about state-of-the-art methods and software for the fast and accurate numerical simulation of physical systems, starting from their fundamental components (linear solve, interpolation, differentiation, quadrature) and building up to ODE solvers.

Physical phenomena are often described in terms of ordinary and partial differential equations (ODEs and PDEs) with interactions and features on multiple scales. Some of these systems are notoriously hard to solve but are of great interest in scientific and engineering applications. In this course you will learn about state-of-the-art methods and software for the fast numerical solution of such systems, focusing on several types of oscillatory ODEs and PDEs in complex geometric settings. We will cover hybrid methods for oscillatory and stiff ODEs, asymptotic approximations, specialized quadrature methods for numerical integration, and introduce powerful boundary integral-based methods for PDEs. We will review famous publications and use both long-standing and cutting edge software packages.

Focuses on discretization techniques such as finite difference, finite element and finite volume methods, and parallel solution algorithms such as Krylov subspace methods, domain decomposition and multilevel methods.

Physical phenomena are often described in terms of ordinary and partial differential equations (ODEs and PDEs) with interactions and features on multiple scales. Some of these systems are notoriously hard to solve but are of great interest in scientific and engineering applications. In this course you will learn about state-of-the-art methods and software for the fast numerical solution of such systems, focusing on several types of oscillatory ODEs and PDEs in complex geometric settings. We will cover hybrid methods for oscillatory and stiff ODEs, asymptotic approximations, specialized quadrature methods for numerical integration, and introduce powerful boundary integral-based methods for PDEs. We will review famous publications and use both long-standing and cutting edge software packages.