Integration of reliable algorithms into modeling software

In this note we discuss strategies that would enhance modern modeling and simulation software (MSS) with reliable routines using validated data types, controlled rounding, algorithmic differentiation and interval equation or initial value problem solver. Several target systems are highlighted. In stochastic traffic modeling, the computation of workload distributions plays a prominent role since they influence the quality of service parameters. INoWaTIV is a workload analysis tool that uses two different techniques: the polynomial factorization approach and the Wiener-Hopf factorization to determine the work-load distributions of GI/GI/1 and SMP/GI/1 service systems accurately. Two extensions of a multibody modeling and simulation software were developed to model kinematic and dynamic properties of multibody systems in a validated way. Furthermore, an interface was created that allows the computation of convex hulls and reliable lower bounds for the distances between subpav-ing-encoded objects constructed with SIVIA (Set Inverter Via Interval Analysis)

Interval algorithms in modelling of multibody systems

Abstract. We will show how a variety of interval algorithms have found their use in the multibody modeling program MOBILE. This paper acquaints the reader with the key features of this open source software, describes how interval arithmetic help to implement new transmission elements, and reports on interval modeling of dynamics, which is an inherent part of multibody simulations. In the latter case, the interval extension of MOBILE enhanced with an interval initial value problem solver (based on VNODE) is presented. The functionality of this application is shown with some examples. We provide insights into techniques used to enhance already existing modeling software with interval arithmetic concepts