Optimization Methods for One Dimensional Elastodynamics Article Swipe

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Discretization Finite element method Mathematical optimization Scheme (mathematics) Conservation law Descent (aeronautics) Mathematics Gradient descent Galerkin method Applied mathematics Optimization problem Computer science Mathematical analysis Physics Meteorology Machine learning Thermodynamics Artificial neural network

Theodoros Katsaounis , G. Kounadis , Ioanna Mousikou , Athanasios E. Tzavaras ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2208.13657 · OA: W4293819480

We propose a new approach for solving systems of conservation laws that admit a variational formulation of the time-discretized form, and encompasses the p-system or the system of elastodynamics. The approach consists of using constrained gradient descent for solving an implicit scheme with variational formulation, while discontinuous Galerkin finite element methods is used for the spatial discretization. The resulting optimization scheme performs well, it has an advantage on how it handles oscillations near shocks, and a disadvantage in computational cost, which can be partly alleviated by using techniques on step selection from optimization methods.