Model Order Reduction for Pattern Formation in FitzHugh-Nagumo Equation
This work provides an efficient computational method for simulating pattern formation in a specific reaction-diffusion system, but is incremental as it applies existing ROM techniques to a particular equation.
The authors developed a reduced order model using POD-DEIM to efficiently compute labyrinth and spot patterns in the FitzHugh-Nagumo equation, achieving accurate pattern formation with few modes and significant computational cost reduction due to the discontinuous Galerkin discretization.
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 POD-DEIM 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.