Blog
About

429
views
0
recommends
+1 Recommend
2 collections
    51
    shares
      • Record: found
      • Abstract: found
      • Poster: found
      Is Open Access

      Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equation

      ScienceOpen Posters

      ScienceOpen

      This work has been published open access under Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com.

      FitzHugh–Nagumo equations, Gradient systems, Traveling fronts and pulses, Turing patterns , Energy preservation, Discontinuous Galerkin, Model order reduction, Discrete empirical interpolation

      Read this article at

      Bookmark
          There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

          Abstract

          We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space by the discontinuous Galerkin (dG) method and in time by the backward Euler method. Applying POD-DEIM (discrete empirical interpolation method) to the full order model (FOM) for different values of the parameter in the bistable nonlinearity, we show that using few POD and DEIM modes, the patterns can be computed accurately. Due to the local nature of the dG discretization, the PODDEIM requires less number of connected nodes than continuous finite element for the nonlinear terms, which leads to a significant reduction of the computational cost for dG POD-DEIM.

          Related collections

          Author and article information

          Journal
          10.14293/P2199-8442.1.SOP-MATH.PMWYZM.v1

          Comments

          Comment on this article