We apply the Local Discontinuous Galerkin discretisation to flow equations of the O(N)-model in the Local Potential Approximation. The improved stability is directly observed by solving the flow equation for various N and space-time dimensions d. A particular focus of this work is the numerical discretisation and its implementation. The code is publicly available, and is explained in detail here. It is realised as a module within the high performance PDE framework DUNE.
F. Ihssen, J. M. Pawlowski, F. R. Sattler, N. Wink, “Local Discontinuous Galerkin for the Functional Renormalisation Group”, arXiv:2207.12266 (2022).
Related to Project A01, A02, C03