A robust procedure for discontinuity handling in continuous system simulation
Transactions of the Society for Computer Simulation International
State event in combined simulation
WSC '88 Proceedings of the 20th conference on Winter simulation
Solving Ordinary Differential Equations with Discontinuities
ACM Transactions on Mathematical Software (TOMS)
The time and state relationships in simulation modeling
Communications of the ACM - Special issue on simulation modeling and statistical computing
Hybrid Systems
Modeling, simulation, sensitivity analysis, and optimization of hybrid systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
An Overview of Hybrid Simulation Phenomena and Their Support by Simulation Packages
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
Accurate Event Detection for Simulating Hybrid Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Modeling of Continuous-Discrete Processes
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Optimal control of flow with discontinuities
Journal of Computational Physics
An asynchronous integration and event detection algorithm for simulating multi-agent hybrid systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A state event detection algorithm for numerically simulating hybrid systems with model singularities
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Finding Errors of Hybrid Systems by Optimising an Abstraction-Based Quality Estimate
TAP '09 Proceedings of the 3rd International Conference on Tests and Proofs
Thermal analysis of multiprocessor SoC applications by simulation and verification
ACM Transactions on Design Automation of Electronic Systems (TODAES)
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Operational semantics of hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Improved relaxations for the parametric solutions of ODEs using differential inequalities
Journal of Global Optimization
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An efficient discontinuity handling algorithm for initial value problems in differential-algebraic equations is presented. The algorithm supports flexible representation of state conditions in propositional logic, and guarantees the location of all state events in strict time order. The algorithm consists of two phases:(1) event detection and(2) consistent event location. In the event detection phase, the entire integration step is searched for the state event by solving the interpolation polynomials for the discontinuity functions generated by the BDF method. An efficient hierarchical polynomial root-finding procedure based upon interval arithmetic guarantees detection of the state event even if multiple state condition transitions exist in an integration step, in which case many existing algorithms may fail. As a second phase of the algorithm, a consistent even location calculation is developed that accurately locates the state event detected earlier while completely eliminating incorrect reactivation of the same state event immediately after the consistent initialization calculation that may follow. This numerical phenomenon has not been explained before and is termed discontinuity sticking. Results from various test problems are presented to demonstrate the correctness and efficiency of the algorithm.