Efficiently solving large-scale electrostatic lightning problems by integrating characteristic basis functions into boundary element method.

The evaluation of the electric field near objects of complex geometries is critical in the pre-bridging regime of lightning strikes in high-voltage transmission systems, which is subject to an open domain problem and can be computationally expensive. In this paper, the characteristic basis function method (CBFM) is incorporated into the conventional boundary element method (BEM) to efficiently handle large-scale electrostatic problems. Within the CBFM, low-level basis functions have been replaced by high-level macro characteristic basis functions, resulting in a significant reduction in the number of degrees of freedom. This reduction in unknowns allows iteration-free direct solvers to approximate the matrices, further reducing the computational complexity of the problem. Numerical examples of the surface charge distribution of an actual 500 kV tower-transmission-line system and a three MW wind turbine in the lightning environment demonstrate the accuracy of the proposed CBFM, while requiring considerably much fewer computational resources compared with conventional BEM. Furthermore, CBFM is highly parallelizable, implying the feasibility of handling large electrostatic lightning problems with complex geometries. [Display omitted] • Derive boundary integral equation of dielectric interfaces in lightning environment. • Introduce characteristic basis function method tailored for electrostatic problems. • Propose strategies of generating characteristic basis functions for electrostatics. • Demonstrate algorithm's time/space complexities, parallelism, and high efficiency. • Derive methods for electric field on boundaries involving strong singular integral. [ABSTRACT FROM AUTHOR]

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