Structure-Preserving Discretizations and their Applications

2024 2027

There is a dedicated CRG Website for this CRG, please see that site for  up to date information.

Nature abounds with mathematical structure. Computational models of nature, however, often do not reflect such structure, and hence their predictions may suffer. Structure-preserving discretizations are numerical methods that attempt to mimic mathematical structures or properties of the continuous system on the discrete (numerical) level. Such discretizations are often essential in order to maintain the accuracy and stability of simulations. Important applications whose predictions hinge on structure preservation include climate modelling, fusion, and turbulence. These applications are linked to some of the most pressing current societal issues. Moreover, emergent applications that utilize machine learning techniques can also benefit from incorporating structure-preserving ideas to improve their prediction and generalizability.

  • Jingwei Hu, University of Washington
  • Steven Ruuth, Simon Fraser University
  • Raymond Spiteri, University of Saskatchewan
  • Andy Wan, University of California, Merced

This CRG will bring together research specialists in structure-preserving discretizations to share their knowledge, expertise, and current challenges in their respective fields. We propose various activities to foster collaboration within and beyond the PIMS network, including a Summer School, Industry Event, two Research Workshops, a 5-day BIRS workshop, two PIMS-wide graduate courses, and a CRG seminar series. We also plan to host 6 long-term visitors and train 2 postdoctoral fellows.

For up to date details of the activities of this CRG, please see their Structure Preserving Discretizations CRG website.

Associate Professor of Applied Mathematics, University of Washington
University of Saskatchewan
McGill University