10 papers
Adaptive singularity swap quadrature for near-singular layer potentials on axisymmetric surfaces
David Krantz, Anna-Karin Tornberg
When numerically evaluating layer potentials at target points close to the domain boundary, specialized quadrature techniques are required for accuracy because of rapid variations…
Fast unified evaluation of layer and volume potentials for the 2D modified Helmholtz equation
Edith Frisk Gärtner, Fredrik Fryklund, Anna-Karin Tornberg
We present a fast and accurate potential theory-based method for the two-dimensional modified Helmholtz equation, treating the involved singular and nearly singular layer evaluatio…
Fast summation on rectangular cuboids with arbitrary periodicity in the DMK framework
David Krantz, Ludvig af Klinteberg, Anna-Karin Tornberg
Dual-space multilevel kernel-splitting (DMK) is a fast summation framework that combines ideas from the fast multipole method, Ewald summation, and multilevel summation. Originally…
Preconditioning for near-contacts in large 2D Stokes flows: a locally compressed method of fundamental solutions
Anna Broms, Anna-Karin Tornberg, Alex H. Barnett
We tackle two key difficulties in the simulation of the viscous hydrodynamics of a large dense collection of rigid particles: (i) the poor convergence rate of an iterative solution…
Stabilizing the singularity swap quadrature for near-singular line integrals
David Krantz, Alex H. Barnett, Anna-Karin Tornberg
Singularity swap quadrature (SSQ) is an effective method for the evaluation at nearby targets of potentials due to densities on curves in three dimensions. While highly accurate in…
Fast Ewald Summation using Prolate Spheroidal Wave Functions
Erik Boström, Anna-Karin Tornberg, Ludvig af Klinteberg
Fast Ewald summation efficiently evaluates Coulomb interactions and is widely used in molecular dynamics simulations. It is based on a split into a short-range and a long-range par…