Partial Differential Equations

Katerina Nik

Assistant Professor, Applied Mathematics and Computational Sciences

Partial Differential Equations free boundary problems calculus of variations Mathematical Biology Microelectromechanical fluid dynamics mean curvature flow

Professor Nik studies partial differential equations that describe phenomena in biological growth processes, fluid dynamics, and mechanical engineering.

Tensor-train Methods for Partial Differential Equations and its application to a Neutron Transport Problem

Daniele Boffi, Associate Dean for Faculty, Computer, Electrical and Mathematical Sciences and Engineering

Nov 14, 15:30 - 17:00

B9 L4 R4225

Partial Differential Equations

Tensor network techniques are known for their ability to approximate low-rank structures and beat the curse of dimensionality. They are also increasingly acknowledged as fundamental mathematical tools for efficiently solving high-dimensional Partial Differential Equations (PDEs). In this talk, we present a novel method that incorporates the Tensor Train (TT) and Quantized Tensor Train (QTT) formats for the computational resolution of time-independent Boltzmann Neutron Transport equations (BNTEs) in Cartesian coordinates.