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The Waveform Relaxation Method For Systems Of Differential/Algebraic Equations, Marija D. Ilić, Mariesa Crow
The Waveform Relaxation Method For Systems Of Differential/Algebraic Equations, Marija D. Ilić, Mariesa Crow
Electrical and Computer Engineering Faculty Research & Creative Works
An extension of the waveform relaxation (WR) algorithm to systems of differential/algebraic equations (DAE) is presented. Although this type of application has been explored earlier in relation to VLSI circuits, the algorithm has not been generalized to include the vast array of DAE system structures. The solvability and convergence requirements of the WR algorithm for higher-index systems are established. Many systems in robotics and control applications are modeled with DAE systems having an index greater than two. Computer simulation of these systems has been hampered by numerical integration methods which perform poorly and must be explicitly tailored to the system. …
The Parallel Implementation Of The Waveform Relaxation Method For The Simulation Of Structure-Preserved Power Systems, Marija D. Ilić, Mariesa Crow
The Parallel Implementation Of The Waveform Relaxation Method For The Simulation Of Structure-Preserved Power Systems, Marija D. Ilić, Mariesa Crow
Electrical and Computer Engineering Faculty Research & Creative Works
Several results pertaining to the partitioning of the waveform relaxation (WR) algorithm for dynamic simulation are presented. The WR algorithm is extended to a structure-preserving power system model in which the loads are retained. This results in a system of differential/algebraic equations (DAEs). Power systems are shown to exhibit several dynamic characteristics which make them suitable for simulation by the WR method. A heuristic method for determining a fault-dependent partitioning of the power system for parallel implementation is given.