Newtonian potentials and gradients for tensor Legendre polynomials on a square satisfy explicit Sylvester equations with low-rank inhomogeneity, giving recurrence-based exact evaluation of singular integrals.
Atkinson, The numerical evaluation of particular solutions for Poisson ’s equation , IMA J
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Newtonian potentials of Legendre polynomials on rectangles have displacement structure
Newtonian potentials and gradients for tensor Legendre polynomials on a square satisfy explicit Sylvester equations with low-rank inhomogeneity, giving recurrence-based exact evaluation of singular integrals.