Doctoral thesis
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Asymptotic analysis of optimized waveform relaxation methods for RC circuits and RLCG transmission lines

Defense date2020-01-28
Abstract

Waveform Relaxation (WR) methods are iterative methods to solve time-dependent problems and large systems of ordinary differential equations arising from large scale electronic circuits. These methods are based on partitioning large circuits into smaller sub-circuits, which are then solved separately for multiple time steps and the overall solution is obtained by iteration between sub-circuits. The slow convergence of these methods especially for large time windows led to the introduction of Optimized Waveform relaxation (OWR) methods, which are based on optimizing parameters. In this thesis, we study the application of these methods to infinite RC and RLCG type circuits. We consider both the overlapping and nonoverlapping WR methods and find the optimized parameters in the transmission conditions. We then developed a novel algorithm that is based on model order reduction techniques for the simplified analysis of OWR methods when applied to infinitely long electric circuits.

Keywords
  • Waveform Relaxation Methods
  • Optimized Waveform Relaxation Methods
  • Domain Decomposition Methods
  • Electric Circuits
  • Time Parallel Methods
Research groups
Citation (ISO format)
KUMBHAR, Pratik Mahadeo. Asymptotic analysis of optimized waveform relaxation methods for RC circuits and RLCG transmission lines. Doctoral Thesis, 2020. doi: 10.13097/archive-ouverte/unige:136729
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Creation03/03/2020 2:50:00 PM
First validation03/03/2020 2:50:00 PM
Update time03/07/2024 8:48:33 AM
Status update03/07/2024 8:48:33 AM
Last indexation10/31/2024 6:50:05 PM
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