6 papers
Singularity swap quadrature for nearly singular line integrals on closed curves in two dimensions
Ludvig af Klinteberg
This paper presents a quadrature method for evaluating layer potentials in two dimensions close to periodic boundaries, discretized using the trapezoidal rule. It is an extension o…
An adaptive kernel-split quadrature method for parameter-dependent layer potentials
Fredrik Fryklund, Ludvig af Klinteberg, Anna-Karin Tornberg
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimens…
Accurate quadrature of nearly singular line integrals in two and three dimensions by singularity swapping
Ludvig af Klinteberg, Alex H. Barnett
The method of Helsing and co-workers evaluates Laplace and related layer potentials generated by a panel (composite) quadrature on a curve, efficiently and with high-order accuracy…
A Fast Integral Equation Method for the Two-Dimensional Navier-Stokes Equations
Ludvig af Klinteberg, Travis Askham, Mary Catherine Kropinski
The integral equation approach to partial differential equations (PDEs) provides significant advantages in the numerical solution of the incompressible Navier-Stokes equations. In…
A parallel non-uniform fast Fourier transform library based on an "exponential of semicircle" kernel
Alex H. Barnett, Jeremy F. Magland, Ludvig af Klinteberg
The nonuniform fast Fourier transform (NUFFT) generalizes the FFT to off-grid data. Its many applications include image reconstruction, data analysis, and the numerical solution of…
Ewald summation for the rotlet singularity of Stokes flow
Ludvig af Klinteberg
Ewald summation is an efficient method for computing the periodic sums that appear when considering the Green's functions of Stokes flow together with periodic boundary conditions.…