Publications Details

Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients

Vuchkov, Radoslav G.; Roberts, Nathan V.; De, Saibal; Alexandrov, Boian; Truong, Duc P.; De Santis, Derek; Rasmussen, Kim O.; Adak, Dibyendu

This manuscript we present a new method for solving PDEs. The method utilizes a mixed formulation of Tensor Train (TT) and Quantized Tensor Train (QTT), designed for the spectral element discretization (Q1-SEM) of the time-dependent convection-diffusion-reaction (CDR) equation. We reformulate the assembly process of the spectral element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the spectral element operators.