Implementation of an Index-3 Differential-Algebraic Equation Solver on Parallel Architecture

A screen grab of a simulation with balls being caught in a netThe Absolute Nodal Coordinate Formulation (ANCF) has been widely used to carry out the dynamics analysis of flexible bodies that undergo large rotation and large deformation. This formulation is consistent with the nonlinear theory of continuum mechanics and is computationally more efficient compared to other nonlinear finite element formulations. Kinematic constraints that represent mechanical joints and specified motion trajectories can be introduced to make complex flexible mechanisms. As the complexity of a mechanism increases, the system of differential algebraic equations becomes very large and results in a computational bottleneck. This project helps alleviate this bottleneck using three tools: (1) an implicit time-stepping algorithm, (2) fine-grained parallel processing on the Graphics Processing Unit (GPU), and (3) enabling parallelism through a novel Constraint-Based Mesh (CBM) approach. The combination of these tools results in a fast solution process that scales linearly for large numbers of elements, allowing meaningful engineering problems to be solved.

Contributors: Daniel Melanz, Radu Serban, Ang Li and Dan Negrut