Zobrazeno 1 - 10
of 110
pro vyhledávání: '"Uzunca, Murat"'
Autor:
Uzunca, Murat, Karasözen, Bülent
Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the Hamiltonia
Externí odkaz:
http://arxiv.org/abs/2309.14184
Autor:
Uzunca, Murat, Karasözen, Bülent
In this paper, reduced-order models (ROMs) are constructed for the Ablowitz-Ladik equation (ALE), an integrable semi-discretization of the nonlinear Schr\"{o}dinger equation (NLSE) with and without damping. Both ALEs are non-canonical conservative an
Externí odkaz:
http://arxiv.org/abs/2207.11130
Publikováno v:
Applied Mathematics and Computation 436 (2023) 127483
Many Hamiltonian systems can be recast in multi-symplectic form. We develop a reduced-order model (ROM) for multi-symplectic Hamiltonian partial differential equations (PDEs) that preserves the global energy. The full-order solutions are obtained by
Externí odkaz:
http://arxiv.org/abs/2203.10933
Publikováno v:
Communications in Nonlinear Science and Numerical Simulation, 115 (2022) 106734
In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting from finite
Externí odkaz:
http://arxiv.org/abs/2109.02075
Publikováno v:
Applied Mathematics and Computation 2022
In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form. Discretization of t
Externí odkaz:
http://arxiv.org/abs/2104.00213
In this paper, Hamiltonian and energy preserving reduced-order models are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with the state-dependent Poisson matrix. The high fidelity full solution
Externí odkaz:
http://arxiv.org/abs/2011.01540
Publikováno v:
Applied Mathematics and Computation, 401, 126058 (2021)
In this work, we present a reduced-order model for a nonlinear cross-diffusion problem from population dynamics, for the Shigesada-Kawasaki-Teramoto (SKT) equation with Lotka-Volterra kinetics. The finite-difference discretization of the SKT equation
Externí odkaz:
http://arxiv.org/abs/2006.07147
Publikováno v:
Computers & Mathematics in Simulation, 2021
Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg de Vries (KdV) equations in Hamiltonian form. The KdV equation is discretized in space by finite differences. The resulting skew-gradient system of o
Externí odkaz:
http://arxiv.org/abs/2004.08509
Publikováno v:
In: Benner P., Breiten T., Fa{\ss}bender H., Hinze M., Stykel T., Zimmermann R. (eds) Model Reduction of Complex Dynamical Systems. International Series of Numerical Mathematics, vol 171. Cham, 2021
An energy preserving reduced order model is developed for the nontraditional shallow water equation (NTSWE) with full Coriolis force. The NTSWE in the noncanonical Hamiltonian/Poisson form is discretized in space by finite differences. The resulting
Externí odkaz:
http://arxiv.org/abs/2002.11719