2023-2024 Women in Mathematics Lecture
Colloquium
Women in Mathematics Lecture
Abstract
Title: Analysis and Simulations of Multidimensional Coupled Problems
Multidimensional coupled problems occur in several applications ranging from geosciences to biomedicine. Drug delivery from the vasculature to the organ, or solute clearance through the lymphatic vessels are two such examples of processes involving flow and transport in networks of 1D vessels embedded in a 3D domain. This talk will first discuss the mathematical and numerical analysis of elliptic partial differential equations with line source. The analysis of such problems is non-standard because the solution exhibits a logarithmic singularity near the 1D line. Convergence of a discontinuous Galerkin method is obtained. Second, we discuss applications of the coupled 3D-1D problems to flow in the liver. With the singularity removal approach, the solution is split into an explicit lower regularity part and a smooth part that can be solved numerically on a uniform mesh.
Beatrice Riviere is the Noah Harding Chair and a Professor in the Department of Computational and Applied Mathematics and Operations Research at Rice University. She has worked extensively on the formulation and analysis of numerical methods applied to problems in porous media and fluid mechanics. She is the author of over one hundred scientific publications in numerical analysis an scientific computation. Her book on the theory and implementation of discontinuous Galerkin methods is highly cited.
Dr. Riviere is a SIAM Fellow (Class of 2021) and an AWM Fellow (Class of 2022). She is also an active member of AWM and USACM and has been involved in SIAM for several decades. Currently, she serves as a member of the SIAM Board of Trustees. She was elected President of the SIAM TX-LA section from 2020 to 2022 and served as Chair of the SIAM Activity Group on Geosciences from 2019 to 2020. She is on the editorial boards of the SIAM Journal on Scientific Computing and Results in Applied Mathematics.
Her current research focuses on developing high-order methods in time and space for flow and transport, the numerical modeling of chemical species transport in blood vessel networks, and the development of neural-based PDE solvers.