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This paper proposes large-scale transient stability simulation based on the massively parallel architecture of multiple graphics processing units (GPUs). A robust and efficient instantaneous relaxation (IR)-based parallel processing technique which features implicit integration, full Newton iteration, and sparse LU-based linear solver is used to run the multiple GPUs simultaneously. This implementation highlights the combination of coarse-grained algorithm-level parallelism with fine-grained data-parallelism of the GPUs to accelerate large-scale transient stability simulation. Multithreaded parallel programming makes the entire implementation highly transparent, scalable, and efficient. Several large test systems are used for the simulation with a maximum size of 9,984 buses and 2,560 synchronous generators all modeled in detail resulting in matrices that are larger than 20\,000\times 20\,000. [ABSTRACT FROM AUTHOR]