high performance computing on graphics processing units: hgpu.org

This paper deals with a Galerkin-based multi-scale time integration of a viscoelastic rope model. Using Hamilton’s dynamical formulation, Newton’s equation of motion as a second-order partial differential equation is transformed into two coupled first order partial differential equations in time. The considered finite viscoelastic deformations are described by means of a deformation-like internal variable determined by a first order ordinary differential equation in time. The corresponding multi-scale time-integration is based on a Petrov-Galerkin approximation of all time evolution equations, leading to a new family of time stepping schemes with different accuracy orders in the state variables. The resulting nonlinear algebraic time evolution equations are solved by a multi-level Newton-Raphson method. Realizing this transient numerical simulation, we also demonstrates a parallelized solution of the viscous evolution equation in CUDA.