2024/08/07 by Sivaram Ambikasaran, Ambikasaran, Sivaram, Ritesh Khan +5
Engineering · Mathematics · Physics and Astronomy · #65R20 #68F55 #68U05 #Applied mathematics #Boundary (topology) #Classical mechanics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Interpolation (computer graphics) #Mathematical analysis #Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Numerical methods in inverse problems #Physics
paper · pdf · doi:10.48550/arxiv.2408.04080
openalex publication_date 2024/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider piecewise polynomial discontinuous Galerkin discretizations of boundary integral reformulations of the heat equation. The resulting linear systems are dense and block-lower triangular and hence can be solved by block forward elimination. For the fast evaluation of the history part, the matrix is subdivided into a family of sub-matrices according to the temporal separation. Separated blocks are approximated by Chebyshev interpolation of the heat kernel in time. For the spatial variable, we propose an adaptive cross approximation (ACA) framework to obtain a data-sparse approximation of the entire matrix. We analyse how the ACA tolerance must be adjusted to the temporal separation and present numerical results for a benchmark problem to confirm the theoretical estimates.