相关论文: Energy conserving nonholonomic integrators

In the last two decades, significant effort has been put in understanding and designing so-called structure-preserving numerical methods for the simulation of mechanical systems. Geometric integrators attempt to preserve the geometry…

We develop a geometric framework for the numerical integration of mechanical systems evolving on manifolds. After briefly reviewing classical numerical methods and highlighting their limitations and shortcomings in non-flat (non-Euclidean)…

For the linearized setting of the dynamics of complex bodies we construct variational integrators and prove their convergence by making use of BV estimates on the rate fields. We allow for peculiar substructural inertia and internal…

We propose and analyze a structure-preserving approximation of the non-isothermal Cahn-Hilliard equation using conforming finite elements for the spatial discretization and a problem-specific mixed explicit-implicit approach for the…

We construct several variational integrators--integrators based on a discrete variational principle--for systems with Lagrangians of the form L = L_A + epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These…

In this paper we propose and investigate a general approach to constructing local energy-preserving algorithms which can be of arbitrarily high order in time for solving Hamiltonian PDEs. This approach is based on the temporal…

This paper develops different discretization schemes for nonholonomic mechanical systems through a discrete geometric approach. The proposed methods are designed to account for the special geometric structure of the nonholonomic motion. Two…

We present a structure preserving discretization of the fundamental spacetime geometric structures of fluid mechanics in the Lagrangian description in 2D and 3D. Based on this, multisymplectic variational integrators are developed for…

This paper formulates variational integrators for finite element discretizations of deformable bodies with heat conduction in the form of finite speed thermal waves. The cornerstone of the construction consists in taking advantage of the…

A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive…

In this paper we study a Hamiltonization procedure for mechanical systems with velocity-depending (nonholonomic) constraints. We first rewrite the nonholonomic equations of motion as Euler-Lagrange equations, with a Lagrangian that follows…

We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…

In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…

In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…

Numerical models of weather and climate critically depend on long-term stability of integrators for systems of hyperbolic conservation laws. While such stability is often obtained from (physical or numerical) dissipation terms, physical…

Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…

In this paper, we introduce a Lagrange multiplier approach to construct linearly implicit energy-preserving schemes of arbitrary order for general Hamiltonian PDEs. Unlike the widely used auxiliary variable methods, this novel approach does…

In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…

A multi-agent system designed to achieve distance-based shape control with flocking behavior can be seen as a mechanical system described by a Lagrangian function and subject to additional external forces. Forced variational integrators are…

In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…