Showing papers by "Andrea Walther published in 2014"

Efficient Implementation of Collocation Methods for Optimization using OpenModelica and ADOL-C

Abstract: Efficient calculation of the solutions of nonlinear optimal control problems (NOCPs) is becoming more and more important for today’s control engineers. The systems to be controlled are typically described using differential-algebraic equations (DAEs), which can be conveniently formulated in Modelica. In addition, the corresponding optimization problem can be expressed using Optimica. Solution algorithms based on collocation methods are highly suitable for discretizing the underlying dynamic model formulation. Thereafter, the corresponding discretized optimization problem can be solved, e.g. by the interior-point optimizer Ipopt. The performance of the optimizer heavily depends on the availability of derivative information for the underlying optimization problem. Typically, the gradient of the objective function, the Jacobian of the DAEs as well as the Hessian matrix of the corresponding Lagrangian formulation need to be determined. If only some or none of these derivatives are provided, usually numerical approximations are used by the optimizer internally. OpenModelica supports the Optimica language and is capable of automatically generating the discretized optimization problem using collocation methods as well as the whole symbolic machinery available. In addition, all necessary derivative information is determined using the automatic differentiation capabilities of ADOL-C, which has now been integrated into the OpenModelica environment.

SCADOPT: An Open-Source HPC Framework for Solving PDE Constrained Optimization Problems Using AD

Abstract: This paper describes SCADOPT, a highly-scalable open-source HPC framework written in C++ for solving PDE constrained optimization problems. The framework is designed to handle explicit time-stepping methods over structured grids for the approximation of time-dependent PDEs. It provides an interface to gradient-based optimization algorithms like L-BFGS-B. Derivatives needed for the optimization are computed via algorithmic differentiation (AD) since this approach provides exact derivatives values with a reasonable computational overhead. Hence, the integration of the AD-tool ADOL-C has been a major design principle for the data management of SCADOPT. We describe the core components of SCADOPT, the employed parallelization methods, and the integration of ADOL-C. Furthermore, we illustrate the solution of an optimization problem based on the heat equation with SCADOPT in about 90 lines. To demonstrate the excellent performance of SCADOPT, we show the weak and strong scaling with respect to MPI on a modern HPC cluster.

Numerical Simulation of the Damping Behavior of Particle-Filled Hollow Spheres

Abstract: In light of an increasing awareness of environmental challenges, extensive research is underway to develop new light-weight materials. A problem arising with these materials is their increased response to vibration. This can be solved using a new composite material that contains embedded hollow spheres that are partially filled with particles. Progress on the adaptation of molecular dynamics towards a particle-based numerical simulation of this material is reported. This includes the treatment of specific boundary conditions and the adaption of the force computation. First results are presented that showcase the damping properties of such particle-filled spheres in a bouncing experiment.