In this paper we consider the numerical solution of the Hamiltonian wave equation in two spatial dimensions. We construct a two step procedure in which we first discretize the space by the Mimetic Finite Difference (MFD) method and then we employ a standard symplectic scheme to integrate the semi-discrete Hamiltonian system derived. The main characteristic of the MFD methods, when applied to stationary problems, is to mimic important properties of the continuous system. This approach yields a full numerical procedure suitable to integrate Hamiltonian problems. A complete theoretical analysis of the method and some numerical simulations are developed in the paper.

Beirao da Veiga, L., Lopez, L., Vacca, G. (2017). Mimetic finite difference methods for Hamiltonian wave equations in 2D. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 74(5), 1123-1141 [10.1016/j.camwa.2017.05.022].

Mimetic finite difference methods for Hamiltonian wave equations in 2D

Beirao da Veiga, L.;Vacca, G.
2017

Abstract

In this paper we consider the numerical solution of the Hamiltonian wave equation in two spatial dimensions. We construct a two step procedure in which we first discretize the space by the Mimetic Finite Difference (MFD) method and then we employ a standard symplectic scheme to integrate the semi-discrete Hamiltonian system derived. The main characteristic of the MFD methods, when applied to stationary problems, is to mimic important properties of the continuous system. This approach yields a full numerical procedure suitable to integrate Hamiltonian problems. A complete theoretical analysis of the method and some numerical simulations are developed in the paper.
Articolo in rivista - Articolo scientifico
Hamiltonian systems; Mimetic finite difference methods; Polygonal meshes;
Hamiltonian systems; Mimetic finite difference methods; Polygonal meshes; Modeling and Simulation; Computational Theory and Mathematics; Computational Mathematics
English
2017
74
5
1123
1141
none
Beirao da Veiga, L., Lopez, L., Vacca, G. (2017). Mimetic finite difference methods for Hamiltonian wave equations in 2D. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 74(5), 1123-1141 [10.1016/j.camwa.2017.05.022].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/178194
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