School of CSE Seminar Series: Jingmei Qiu

Speaker: Jingmei Qiu, professor at the University of Delaware
Date and Time: September 20, 2:00-3:00 p.m.
Location: Coda, 9th Floor Atrium
Host: Florian Schäfer

Title: Low Rank Tensor Methods for High Dimensional Time-Dependent PDEs

Abstract: I will provide an overview of low-rank time integrators for time-dependent PDEs, with a particular focus on kinetic models. These integrators include an explicit method involving time-stepping followed by an SVD truncation procedure, applied to the nonlinear Vlasov model; implicit integrators leveraging extended Krylov subspaces for the Fokker-Planck equation; implicit-explicit low-rank integrators for advection-diffusion equations; and a Semi-Lagrangian Adaptive-Rank Method (SLAR) applied to the Vlasov model. A key feature of our algorithm is its significantly reduced computational complexity, which scales linearly with the number of grid points per dimension and polynomially with respect to the rank. Additionally, we develop Locally Macroscopic Conservative (LoMaC) projections to preserve the underlying macroscopic structure of the kinetic system. A wide range of benchmark tests have been conducted to demonstrate the efficiency and effectiveness of the proposed scheme.

We gratefully acknowledge our collaborators: Dr. Luis Chacon (Los Alamos National Lab), Dr. Andrew Christlieb (Michigan State University), Dr. Lukas Einkemmer (University of Innsbruck), Dr. Daniel Hayes (University of Delaware), Dr. Wei Guo (Texas Tech University), Dr. Nakao Joseph (Swarthmore College), Ph.D. student Hamad Kahza (University of Delaware), William Taitano (Los Alamos National Lab), and Dr. Nanyi Zheng (University of Delaware).

Bio: Dr. Jingmei Qiu is a Unidel Professor in the Department of Mathematical Sciences at the University of Delaware. Her research focuses on the design, analysis, and application of high-order structure-preserving computational algorithms for complex systems characterized by multi-scale, multi-physics, and high-dimensional features. Dr. Qiu’s work includes developing low-rank tensor approximations for high-dimensional, time-dependent problems with structure preservation, as well as Eulerian-Lagrangian high-order numerical methods for fluid and kinetic applications. She was awarded the Air Force Young Investigator Award in 2012 and is the lead Principal Investigator of a Multidisciplinary University Research Initiative (MURI) project on Tensor Networks, supported by the Department of Defense from 2024 to 2029.