Minimal $ \ell^2 $ norm discrete multiplier method
Erick Schulz, Andy T. S. Wan · Journal of Computational Dynamics · 2024
We introduce the Minimal $ \ell^2 $ Norm Discrete Multiplier Method (MN-DMM) to extend the practical applicability of the Discrete Multiplier Method, where conservative finite difference schemes can now be constructed procedurally. This method alleviates the potential need for significant manual effort at deriving globally defined conservative schemes for large dynamical systems with multiple conserved quantities. MN-DMM utilizes the Moore-Penrose pseudoinverse of the discrete multiplier matrix to simultaneously approximate the unique consistent conservative scheme with minimal $ \ell^2 $ norm and its solution. We show the wide applicability of MN-DMM and its relative ease of implementation compared to the original Discrete Multiplier Method on problems such as the planar restricted three-body problem, Lorenz system, three-species Lotka-Volterra systems, spherical point vortex problem, and geodesic curves on Schwarzschild spacetime metric.