Integrating the Integrators for Nonlinear Evolution Equations: from Analysis to Numerical Methods, High-Performance-Computing and Applications (18w5152)

Arriving in Banff, Alberta Sunday, December 2 and departing Friday December 7, 2018

Organizers

(University of Innsbruck)

Mayya Tokman (University of California, Merced)

Objectives

This workshop will bring together researchers from the analysis, numerics, HPC and applications communities to spur discussions and collaborations leading to the next generation of numerical integrators for nonlinear evolution equations. An important aim of the workshop is to facilitate and foster a dialogue between scientists working on analytical and numerical techniques and those focused on practical implementation and application of these methods. The workshop will help practitioners learn of the latest innovations in numerical integrators and inform analysts of specific demands that cutting edge applications impose on new methods. The meeting will also provide a platform for exchange of ideas and new approaches in the field of nonlinear evolution equations from across analysis, numerics and HPC. The conference will include keynote lectures from experts who will provide overviews of their fields and outline open questions. In addition, more focused sessions will be organized that focus on specific types of problems and application fields (e.g. wave phenomena, stiff problems arising in fluid dynamics, plasma physics and climate modeling, etc.) and different classes of integrators (e.g. splitting, geometric, exponential, etc.). Particular attention will be paid to structuring the workshop to promote interdisciplinarity. Each session will include talks on theoretical and practical aspects of classes of problems (e.g. reaction-advection-diffusion systems, magnetohydrodynamic and Navier-Stokes equations, kinetic models such as Vlasov equations) as well as relevant numerical integration techniques, HPC algorithms and software. In scheduling the workshop the organizers will also aim to leave considerable amount of time outside of lectures to enable discussions that will help identify cross-over areas and problems requiring input from several communities.



An obstacle to bridging different research communities is the lack of knowledge on respective literature and availability of software from the different fields. One objective of the workshop will be a discussion of possible ideas to amend this problem. In particular, an important outcome of the workshop will be a repository of relevant papers, software and reference materials created with the help of all workshop participants. At the workshop the idea of extending and maintaining such a repository will be discussed and materials will be provided by the community. The organizers will then use the feedback from the community to assess the best structural and technical ways to create and maintain such a repository. In addition, the conference will include a discussion of a plan for future workshops and conferences dedicated to the subject.



Another important goal of the workshop is providing learning and networking opportunities for the next generation of researchers. Nearly a quarter of participants will include researchers at early stages in their careers (graduate students, postdocs and junior faculty members). The workshop will enable these attendees to form new interdisciplinary collaborations or join existing ones, learn from experts in the fields about open questions and promote their ideas and research.