A broad range of scientific simulations involve solving large-scale computationally expensive linear systems of equations. Iterative solvers are typically preferred over direct methods when it comes to large systems due to their lower memory requirements and shorter execution times. However, selecting the appropriate iterative solver is problem-specific and dependent on the type and symmetry of the coefficient matrix. Gauss-Seidel (GS) is an iterative method for solving linear systems that are either strictly diagonally dominant or symmetric positive definite. This technique is an improved version of Jacobi and typically converges in fewer iterations. However, the sequential nature of this algorithm complicates the parallel extraction. In fact, most parallel derivatives of GS rely on the sparsity pattern of the coefficient matrix and require matrix reordering or domain decomposition. In this article, we introduce a new algorithm that exploits the convergence property of GS and adapts the parallel structure of Jacobi. The proposed method works for both dense and sparse systems and is straightforward to implement. We have examined the performance of our method on multicore and many-core architectures. Experimental results demonstrate the superior performance of the proposed algorithm compared with GS and Jacobi. Additionally, performance comparison with built-in Krylov solvers in MATLAB showed that in terms of time per iteration, Krylov methods perform faster on CPUs, but our approach is significantly better when executed on GPUs. Lastly, we apply our method to solve the power flow problem, and the results indicate a significant improvement in runtime, reaching up to 87 times faster speed compared with GS.

This paper presents the development of an intelligent dynamic energy management system (I-DEMS) for a smart microgrid. An evolutionary adaptive dynamic programming and reinforcement learning framework is introduced for evolving the I-DEMS online. The I-DEMS is an optimal or near-optimal DEMS capable of performing grid-connected and islanded microgrid operations. The primary sources of energy are sustainable, green, and environmentally friendly renewable energy systems (RESs), e.g., wind and solar; however, these forms of energy are uncertain and nondispatchable. Backup battery energy storage and thermal generation were used to overcome these challenges. Using the I-DEMS to schedule dispatches allowed the RESs and energy storage devices to be utilized to their maximum in order to supply the critical load at all times. Based on the microgrid's system states, the I-DEMS generates energy dispatch control signals, while a forward-looking network evaluates the dispatched control signals over time. Typical results are presented for varying generation and load profiles, and the performance of I-DEMS is compared with that of a decision tree approach-based DEMS (D-DEMS). The robust performance of the I-DEMS was illustrated by examining microgrid operations under different battery energy storage conditions.