Time Integrators Based on Approximate Discontinuous Hamiltonians

Abstract eng:
In this talk we present a class of time integration algorithms for systems with separable Hamiltonians. By partitioning the system’s configuration space to construct an approximate potential energy, we define an approximate discontinuous Hamiltonian (ADH) whose resulting equations of motion can be solved exactly. The ADH scheme proposed gives rise to an explicit class of time integrators that are scalable, unconditionally stable and possess good conservation properties. In addition, this class of integrators is naturally asynchronous and can be easily extended to handle contact problems and nearly incompressible materials. We demonstrate our method with several problems from solid mechanics such as a rotating bodies and multiple collisions of bodies with rigid boundaries.

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