By Negin Bagherpour, Peter Gangl, Francesco Ludovici, Petar Sapun, and Erin M. Kiley
From August 4 through 15, 45 students representing six continents took part in the Gene Golub SIAM Summer School, held at RICAM, the Radon Institute for Computational and Applied Mathematics, on the campus of Johannes Kepler University in Linz, Austria.
Linz is a small, beautiful, and historic city in Upper Austria. As the home of Johannes Kepler, it provided a germane as well as picturesque setting for the Summer School: The view of its famed Pöstlingberg emerging from morning fog on the hill is not something that any of the participants will forget. A guided city tour on the first day taught participants––locals and visitors alike––about Linz’s rich history and cultural significance within central Europe. Another highlight was a visit that evening to the OK (Offenes Kulturhaus), where interactive installations transported participants and organizers back to childhood––a light-hearted environment perfect for getting to know each other on our first day together.
The technical program consisted of four main lecture tracks, in addition to a guest lecture. We students were given the opportunity to “roll up our sleeves” and, with guidance from the lecturers themselves, tackle both “paper and pencil” and computational exercises designed to complement the lecture material.
Michael Stingl (University of Erlangen-Nürnberg) delivered lectures on topological and material optimization, including an extended example on elastic beam deformation, which provided context for the existence and convergence results presented in the lectures.
Esther Klann (JKU, Linz) introduced students to the study of inverse problems, including regularization methods and shape sensitivity analysis. She gave an extended example from the field of tomography, and her corresponding computational exercises included several real demonstrations supporting her final appeal: “Do not go out there and commit an inverse crime!”
Roland Herzog (TU Chemnitz) discussed optimization subject to complementarity constraints, with topics that included elastoplasticity and the obstacle problem, along with exercises on the energy minimization of cable car configurations given the shape of the underlying landscape (inspiring heights of creativity as students designed interesting mountains!).
Real-world applications: Summer School students considered the optimal positions of three pylons (triangles) supporting the weight of a cable car, together with the forces exerted by the pylons. The pylons are positioned in such a way that the vertical components of the forces required at the foot and top of the mountain are minimized.
Winnifried Wollner (University of Hamburg) gave a thorough and self-contained introduction to adaptive finite element methods, with computational demonstrations of both the advantages and––when not thoughtfully implemented––the disadvantages of adaptive meshing; he also offered strategies for ameliorating the most common problems that arise in implementation. Topics included convergence, error estimates, and application to optimization problems.
We were also fortunate to have a guest lecturer––Jakob Søndergaard Jensen (Center for Acoustic-Mechanical Micro Systems, TU Denmark), who devoted his three-hour lecture to the application of topology optimization to dynamics of materials and structures. Along with the classic problems of optimal material design and topology optimization in photonics, he covered recent applications of robust acoustic topology optimization and nonlinear topology optimization.
Over the weekend, we all experienced “science in action” on a visit to Linz’s world-famous steel plant, owned and operated by voestalpine AG. Other highlights were a cruise on the Danube in the beautiful Wachau Valley preceding a visit to the Melk monastery.
Summer School students and lecturers during a visit to the steel-making facility of voestalpine AG in Linz.
The thoughtful organization of every aspect of the summer school, technical and social alike, made these two weeks a success. The intense atmosphere brought together students and professionals from a diverse range of areas within computational and applied mathematics, in an environment where discussion and learning––guided by energetic and engaging professors––were paramount. The participants are grateful to the organizers, to all of the lecturers, and to SIAM, for making our summer school experience an unforgettable one.
Summer School lecturers in the garden of the Melk monastery. From left: Roland Herzog, Esther Klann, Winnifried Wollner, and Michael Stingl.
2015 Golub Summer School Slated for Delphi, Greece
Randomization in numerical linear algebra is the topic of the sixth Gene Golub SIAM Summer School, which will be held in Delphi, Greece. This new research area is highly interdisciplinary, with contributions from numerical linear algebra, theoretical computer science, scientific computing, statistics, optimization, data analysis, and machine learning, and such application areas as genetics, physics, astronomy, and Internet modeling. Students will thus be selected from a wide range of backgrounds.
The organizers are Petros Drineas, Rensselaer Polytechnic Institute, USA; Efstratios Gallopoulos, University of Patras, Greece (the host institution); Ilse Ipsen, North Carolina State University, USA; and Michael Mahoney, University of California at Berkeley, USA.
The application deadline is February 1, 2015. Further information will be posted as available here.
Negin Bagherpour is a Ph.D student in applied mathematics at the Sharif University of Technology. Peter Gangl is a Ph.D. student in the doctoral program on computational mathematics at Johannes Kepler University, Linz. Francesco Ludovici is a Ph.D. student in the Department of Optimization and Approximation at Hamburg University. Petar Sapun is a Ph.D student at the University of Hamburg. Erin M. Kiley is a graduate student at the Worchester Polytechnic Institute.