Energy Stable Model Order Reduction for Gradient Systems

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2016-03-30

Author

Karasözen, Bülent

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https://hdl.handle.net/11511/85334

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Energy Stable Discontinuous Galerkin Finite Element Method for the Allen-Cahn Equation Karasözen, Bülent; Sariaydin-Filibelioglu, Ayse; Yücel, Hamdullah (2018-05-01) In this paper, we investigate numerical solution of Allen-Cahn equation with constant and degenerate mobility, and with polynomial and logarithmic energy functionals. We discretize the model equation by symmetric interior penalty Galerkin (SIPG) method in space, and by average vector field (AVF) method in time. We show that the energy stable AVF method as the time integrator for gradient systems like the Allen-Cahn equation satisfies the energy decreasing property for fully discrete scheme. Numerical result...
Energy preserving model order reduction of the nonlinear Schrodinger equation Karasözen, Bülent (2018-12-01) An energy preserving reduced order model is developed for two dimensional nonlinear Schrodinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE is discretized in space by the symmetric interior penalty discontinuous Galerkin (SIPG) method. The resulting system of Hamiltonian ordinary differential equations are integrated in time by the energy preserving average vector field (AVF) method. The mass and energy preserving reduced order model (ROM) is constructed by proper orth...
Energy Stable Interior Penalty Discontinuous Galerkin Finite Element Method for Cahn-Hilliard Equation Sariaydin-Filibelioglu, Ayse; Karasözen, Bülent; Uzunca, Murat (2017-08-01) An energy stable conservative method is developed for the Cahn-Hilliard (CH) equation with the degenerate mobility. The CH equation is discretized in space with the mass conserving symmetric interior penalty discontinuous Galerkin (SIPG) method. The resulting semi-discrete nonlinear system of ordinary differential equations are solved in time by the unconditionally energy stable average vector field (AVF) method. We prove that the AVF method preserves the energy decreasing property of the fully discretized ...
Energy preserving reduced-order modeling of the rotating thermal shallow water equation Karasözen, Bülent; Ylldlz, S.; Uzunca, M. (2022-05-01) © 2022 Author(s).In this paper, reduced-order models (ROMs) are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with state-dependent Poisson matrix. The high fidelity full solutions are obtained by discretizing the RTSWE in space with skew-symmetric finite-differences, while preserving the Hamiltonian structure. The resulting skew-gradient system is integrated in time by the energy preserving average vector field (AVF) method. The ROM is constructed by...
Energy preserving methods for lattice equations Erdem, Özge; Karasözen, Bülent (2010-11-27) Integral preserving methods, like the averaged vector field, discrete gradient and trapezoidal methods are to Poisson systems. Numerical experiments on the Volterra equations and integrable discretization of the nonlinear Schrodinger equation are presented.

Citation Formats

B. Karasözen, “Energy Stable Model Order Reduction for Gradient Systems,” 2016, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/85334.