DOE OSTI · 2997365
Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients
Abstract
In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.
Explore related subjects
Keep this discovery
Explore connections, maps & timelines
Adak, Dibyendu [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000252007074), Truong, Duc P. [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000298063274), Vuchkov, Radoslav [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)] (ORCID:0000000293663465), De, Saibal [Sandia National Lab. (SNL-CA), Livermore, CA (United States)] (ORCID:000000034691189X), DeSantis, Derek [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000176487343), Roberts, Nathan V. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)] (ORCID:0000000315360749), Rasmussen, Kim Ø. [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)], Alexandrov, Boian S. [Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)] (ORCID:0000000186364603). 2025-07-15. Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients. https://doi.org/10.3390/math13142277
Cite the original work for its findings. Save a collection to share your selection of sources.