A Fast Calculation Method for Electrostatic Fields in Complex Terrain Using NSGA-II and Conformal Mapping

Rapid and accurate calculation of lightning-induced electric fields in complex terrain is essential for lightning protection and electromagnetic compatibility analysis. Although conventional full-wave numerical methods such as the finite element method can achieve high-fidelity results, they are computationally expensive and inefficient for large-scale or repetitive engineering analysis. To enable efficient and reliable computation of lightning-induced electrostatic fields over complex terrain, this paper proposes a fast computational framework that integrates multi-level conformal mapping with a multi-objective optimization strategy based on the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). In the proposed method, irregular terrain boundaries are transformed into analytically tractable domains using multi-level conformal mapping, while the critical mapping parameter is reformulated as a dual-objective optimization problem that simultaneously minimizes the maximum local error and the mean global error. Unlike traditional approaches that rely on empirical tuning or exhaustive traversal of mapping parameters, the proposed framework establishes a closed-loop adaptive optimization process that generates a Pareto-optimal solution set, enabling flexible trade-off selection according to practical accuracy requirements. The method is validated against high-fidelity finite element simulations for representative terrain profiles. The results demonstrate that the proposed approach achieves comparable maximum-error performance while reducing mean error and significantly improving parameter-optimization efficiency relative to exhaustive search methods. The proposed framework provides an adaptive and efficient computational solution for preliminary assessment of lightning-induced electric fields in complex terrain environments, and lays a foundation for future extensions toward more realistic multi-dimensional and transient analyses. The improvements in computational accuracy and efficiency offer significant practical value for rapid lightning protection assessment in large-scale complex terrain engineering, enabling parametric analysis and scheme comparison during the preliminary engineering design stage with sufficient reliability.