UTDKernels.jl: A branch-safe and differentiable Julia library for Kouyoumjian–Pathak wedge diffraction kernels

UTDKernels.jl is an open-source Julia package that evaluates the scalar Kouyoumjian–Pathak (KP) wedge diffraction kernels for perfectly electrically conducting (PEC) wedges in a numerically robust, branch-safe, and automatic-differentiation (AD) compatible manner. The library is intentionally scoped to the kernel building block—the soft/hard scalar coefficients D s/h and the transition function F ( x ) in the plane normal to the edge—so it can be embedded in higher-level three-dimensional ray-tracing engines. The transition function is evaluated through the scaled complementary error function erfcx to avoid overflow; the cot ⁡ ( ψ ) F ( X ) = ∞ ⋅ 0 singularity at every shadow boundary is removed by a regularised factored-ratio form; all square roots use a single, documented principal branch; and a package extension supplies the missing erfcx derivative rule for forward-mode AD, making the full kernel differentiable in observation angle, wavenumber, and effective distance. The implementation is validated against the exact Sommerfeld half-plane solution at floating-point round-off and recovers the geometrical theory of diffraction (GTD) limit at the theoretical O ( 1 / k L ) rate.