Space-Time approaches to PDE Solvers: Unlocking the Power of Co-Design (26w5643)

The Banff International Research Station will host the "Space-Time approaches to PDE Solvers: Unlocking the Power of Co-Design" workshop in Banff from November 8 to November 13, 2026.

Space-time methods have emerged as a promising and powerful approach to solving partial differential equations (PDEs) across a broad range of scientific and engineering fields. These methods consider both spatial and temporal discretization simultaneously and hence offer advantages in simulating complex multiscale models where classical ``segregated" approaches may struggle. By treating space and time on a more equal footing, space-time solvers can allow for better accuracy, parallel scalability, and handling of dynamic and adaptive algorithms.

At the same time, the concept of "co-design"—where in this case the consideration of algorithms, hardware, and software architecture is incorporated in tandem at all stages—has been increasingly recognized as a key enabler for maximizing the performance of modern computational methods. Co-design ensures that solvers are optimized not only for accuracy and robustness but also for speed, energy efficiency, and scalability, making it a fundamental strategy in tackling the computational challenges of large-scale PDE-based simulations.

The 5-day workshop, "Space-time Approaches to PDE Solvers: Unlocking the Power of Co-Design'', will bring together a diverse group of leading international experts in numerical analysis, scientific computing, and hardware-software integration to review and explore the cutting-edge developments and challenges in the simulation of complex PDEs. The workshop will focus on three major themes: i) space-time discretization methods for PDEs; ii) co-design principles for the next generation of PDE solvers; and iii) real-world applications for these advanced solvers, ranging from fluid dynamics and Earth system modeling to plasma-based energy systems to biomedical simulations and personalized medicine.

Participants will have the opportunity to discuss recent advances, exchange ideas, and initiate collaborations on new research that unlock the synergies between space-time solvers through the use of co-design. The workshop aims to foster a leading multidisciplinary community that can work together to develop more efficient and scalable solutions for solving PDEs, with the goal of introducing transformative change in how complex simulations are performed across multiple disciplines. By integrating the most recent innovations from algorithmic, software, and applications aspects of PDE solvers, this workshop promises to unlock new possibilities for tackling some of the most challenging computational problems of our time.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF) and Alberta's Technology and Innovation.