Implicit Dynamical low-rank Discontinuous Galerkin Methods for Space Homogeneous Neutrino Transport Equations

Abstract: Neutrino transport plays an important role in core-collapse supernova (CCSN) explosions. Due to the multiscale nature of neutrino transport in CCSN simulations, an implicit treatment is desired. The equations are high dimensional and their solutions can converge to isotropic equilibrium distributions, which are low dimensional, in regions of high Knudsen number. We propose implicit dynamical low-rank discontinuous Galerkin (DLR-DG) methods for space homogeneous neutrino transport equations. Compared with the classical DG method, the DLR-DG solution here is a DG approximation with the corresponding coefficient matrix in a rank-$r$ manifold. The proposed DLR-DG method is shown to be stable even for large time steps and has lower computational complexity compared with the classical DG method. Numerical test results are presented to justify the theoretical findings.

Speaker’s Bio: Peimeng Yin is a Postdoctoral Research Associate in Computer Science and Mathematics Division at Oak Ridge National Laboratory (ORNL). He received his Ph.D. in the Department of Mathematics from Iowa State University in 2019. Prior to joining ORNL, he worked as a Post-Doc Fellow in the Department of Mathematics at Wayne State University, and a Research Assistant Professor (research-track) in the Department of Radiation Oncology at the University of Kansas Medical Center. He works in the area of Computational Mathematics and Applied Mathematics with the main focus on Numerical Analysis, Partial Differential Equations, Scientific Computing, and Data Science. His work reflects a strong interplay of rigorous mathematical analysis, the design and implementation of accurate and efficient numerical algorithms for partial differential equations, and their applications to physics, astrophysics, engineering, biology, energy, and oncology.