Synchronization law for a Van der Pol array

We explore the transition to in-phase synchronization in globally coupled oscillator arrays, and compare results for van der Pol arrays with Josephson junction arrays. Our approach yields in each case an analytically tractable iterative map; the resulting stability formulas are simple because the expansion procedure identifies natural parameter groups. A third example, an array of Duffing-Van der Pol oscillators, is found to be of the same fundamental type as the van der Pol arrays, but the Josephson arrays are fundamentally different owing to the absence of self-resonant interactions

GPU-Resident Sparse Direct Linear Solvers for Alternating Current Optimal Power Flow Analysis

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs

GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs