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Leveraging the power of nowadays graphics processing units for robust power grid simulation remains a challenging task. Existing preconditioned iterative methods that require incomplete matrix factorizations can not be effectively accelerated on GPU due to its limited hardware resource as well as data parallel computing. This work presents an efficient GPU-based multigrid preconditioning algorithm for robust power grid analysis. An ELL-like sparse matrix data structure is adopted and implemented specifically for power grid analysis to assure coalesced GPU device memory access and high arithmetic intensity. By combining the fast geometrical multigrid solver with the robust Krylov-subspace iterative solver, power grid DC and transient analysis can be performed efficiently on GPU without loss of accuracy (largest errors < 0.5 mV). Unlike previous GPU-based algorithms that rely on good power grid regularities, the proposed algorithm can be applied for more general power grid structures. Experimental results show that the DC and transient analysis on GPU achieves more than 25X speedups over the best available CPU-based solvers. An industrial power grid with 10.5 million nodes can be accurately solved in 12 seconds.

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The spectral domain approach (SDA) is a full-wave analysis method, which is used to obtain the effective dielectric constant of the microstrip. When the operating frequency decreases to zero, by introducing the normalized transverse current, this method reduces to a generalized eigenvalue problem. In order to obtain an accurate relative dielectric constant, the normalized transverse current should be considered. The Chebyshev polynomials with edge singularity are used as the basis functions for both the normalized transverse current and the longitudinal current. The SDA at dc and the variational method can lead to the same result.Index Terms-Charge distribution, Chebyshev polynomials, current density, spectral domain approach (SDA), variational method.

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