Structure-preserving Algorithms For Beam Vibration Equations

Local structure-preserving algorithms for partial differential equations, which are natural generalization of symplectic algorithms for Hamiltonian ordinary differ-ential equations, enlarges the applicable scopes of structure-preserving algorithm-s. In this thesis, the local structure-preserving algorithms for beam vibration equa-tions are investigated systematically by using the concatenating method. A series of multi-symplectic conservation schemes, the local energy-conserving schemes and local momentum-conserving schemes respectively for beam vibration equations are constructed. Among these schemes, some are existed and widely used, some are new. Some numerical experiments are presented to show the efficiency and superiority of the new constructed algorithms for beam vibration equations.In the field of structure-preserving algorithms, multi-symplectic partitioned Runge-Kutta methods are so important that lots of relative achievements have been made in the numerical simulation of partial differential equations. For two differ-ent multi-symplectic forms of beam vibration equations, two symplectic partitioned Runge-Kutta methods are used to the discrete the equations in space and time respec-tively. We restrictively prove the multi-symplectic conservation laws of the partitioned Runge-Kutta methods for beam vibration equations.