High-order Nyström schemes for efficient 3-D capacitance extraction
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
Nyström-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels
Mathematics of Computation
Journal of Computational Physics
Second kind integral equations for the classical potential theory on open surfaces II
Journal of Computational Physics
A fast direct solver for boundary integral equations in two dimensions
Journal of Computational Physics
Integral and integrable algorithms for a nonlinear shallow-water wave equation
Journal of Computational Physics
A fast direct solver for scattering problems involving elongated structures
Journal of Computational Physics
Quadrature rule for indefinite integral of algebraic-logarithmic singular integrands
Journal of Computational and Applied Mathematics
Fredholm integral equation method for the integro-differential Schrödinger equation
Computers & Mathematics with Applications
High-order quadratures for the solution of scattering problems in two dimensions
Journal of Computational Physics
High-order corrected trapezoidal quadrature rules for the coulomb potential in three dimensions
Computers & Mathematics with Applications
Journal of Computational Physics
High-order quadrature rules based on spline quasi-interpolants and application to integral equations
Applied Numerical Mathematics
Journal of Computational Physics
Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator
Journal of Computational Physics
A Fast Randomized Algorithm for Computing a Hierarchically Semiseparable Representation of a Matrix
SIAM Journal on Matrix Analysis and Applications
Second kind integral equation formulation for the modified biharmonic equation and its applications
Journal of Computational Physics
Quadrature by expansion: A new method for the evaluation of layer potentials
Journal of Computational Physics
Advances in Computational Mathematics
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A class of quadrature formulae is presented applicable to both nonsingular and singular functions, generalizing the classical endpoint corrected trapezoidal quadrature rules. While the latter rules are usually derived by means of the Euler--Maclaurin formula, their generalizations are obtained as solutions of certain systems of linear algebraic equations. A procedure is developed for the construction of very high-order quadrature rules, applicable to functions with a priori specified singularities, and relaxing the requirements on the distribution of nodes. The scheme applies not only to nonsingular functions but also to a wide class of functions with monotonic singularities. Numerical experiments are presented demonstrating the practical usefulness of the new class of quadratures. Tables of quadrature weights are included for singularities of the form $s(x) = |x|^\lambda$ for a variety of values of $\lambda$, and $s(x) = \log{|x|}$.