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We present a generic scheme to construct corrected trapezoidal rules withspectral accuracy for integral operators with weakly singular kernels inarbitrary dimensions. We assume that the kernel factorization of the form,$K=\alpha\phi+\widetilde{K}$ with smooth $\alpha$ and $\widetilde{K}$, isavailable so that the operations on the smooth factors can be performedaccurately on the basis of standard Fourier spectral methods. To achieve highprecision results, our approach utilizes the exact evaluation of the Fouriercoefficients of the radial singularity $\phi$, which can be obtained inarbitrary dimensions by the singularity isolation/truncation described in thisarticle. We provide a complete set of formulas for singularities of the type:$\log(r)$ and $r^{-\nu}$. Convergence analysis shows that the constructedquadrature rules exhibit almost identical rate of convergence to thetrapezoidal rule applied for non-singular integrands. Especially, for smoothdata, the corrected trapezoidal rules converge super-algebraically.

Singular quadrature rules and fast convolutions for Fourier spectral methods