Speaker: Wolfgang Bangerth, Colorado State University

Time : 15:00 - 16:00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

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Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Numerical methods, finite element methods, software libraries

Abstract:  Historically, the numerical methods and numerical analysis community has always been careful to not just develop methods abstractly, but also to demonstrate their performance using numerical examples -- nearly every numerical methods paper has a section that shows the results of concrete simulations. This approach is grounded in the belief that we are developing methods because we want to solve actual problems.

The best papers often demonstrate new methods using test cases that aren't contrived (say, solving a problem on a uniform mesh for the unit square) but taken from concrete applications. At the same time, implementing such test cases is of course a substantial investment if one wants to implement everything from scratch.

In this talk, I will describe the widely-used open source software deal.II [1, 2] that provides tools for finite element discretizations of differential and integral equations deal.II is the basis for nearly 3,000 known publications, of which at least a dozen deal with fractional differential operators. In addition to the library's specific features, I will in particular outline how its many tutorial and code gallery programs can serve as starting points for numerical experiments that include non-trivial geometries, realistic equations, and parallel and advanced linear and nonlinear solver techniques.

Biography: Wolfgang Bangerth is a professor in the Department of Mathematics and (by courtesy) the Department of Geosciences at Colorado State University. His work is mainly concerned with the development of finite element methods for applications throughout the sciences, typically in highly interdisciplinary collaborations. He is a founding member and a principal developer of the widely used deal.II software library (see https://www.dealii.org) that is used in nearly 3,000 publications; and of the Advanced Solver for Planetary Evolution, Convection, and Tectonics (ASPECT, see https://aspect.geodynamics.org/). For his work, he has received the 2007 J. H. Wilkinson Prize for Numerical Software and the 2025 SIAM/ACM Prize in Computational Scienceand Engineering

Bibliography

[1] D. Arndt, W. Bangerth, D. Davydov, T. Heister, L. Heltai, M. Kronbichler, M. Maier, J.-P. Pelteret, B. Turcksin, D. Wells: “The deal.II finite element library: design, features, and insights”. Computers & Mathematics with Applications, vol. 81, pp. 407–422 (2026).