Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
For Zoom Link please contact ddelreyfernandez@uwaterloo.ca
David Williams, Assistant Professor, Department of Mechanical Engineering, Penn State University
Current Challenges for Space-Time Finite Element Methods
Space-time finite element methods (FEMs) are likely to grow in popularity due to the ongoing growth in the size, speed, and parallelism of modern computing platforms. The allure of space-time FEMs is both intuitive and practical. From the intuitive standpoint, there is considerable elegance and simplicity in accommodating both space and time using the same numerical discretization strategy. From the practical standpoint, there are considerable advantages in efficiency and accuracy that can be gained from space-time mesh adaptation: i.e. adapting the mesh in both space and time to resolve important solution features. However, despite these considerable advantages, there are numerous challenges that must be overcome before space-time FEMs can realize their full potential. These challenges are primarily associated with four-dimensional geometric obstacles (hypersurface and hypervolume mesh generation), four-dimensional approximation theory (basis functions and quadrature rules), four-dimensional boundary condition enforcement (well-posed, moving boundary conditions), and iterative-solution techniques for large-scale linear systems. In this presentation, we will provide a brief overview of space-time FEMs, and discuss some of the latest research developments and ongoing issues.
Contact Info
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario
Canada N2L 3G1
Phone: 519-888-4567, ext. 32700
Fax: 519-746-4319
PDF files require Adobe Acrobat Reader
The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within the Office of Indigenous Relations.