28 citations · 30 across the 10 of their papers we have counts for
11 papers
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…
Fourier-based potential theory without an explicit Green's function
Fredrik Fryklund
Integral equation methods provide an effective framework for solving partial differential equations, but their applicability typically relies on the availability of explicit free-s…
Scattering theory for Stokes flow in complex branched structures
Haiyang Wang, Fredrik Fryklund, Samuel Potter +1
Slow, viscous flow in branched structures arises in many biological and engineering settings. Direct numerical simulation of flow in such complicated multi-scale geometry, however,…
A Lightweight, Geometrically Flexible Fast Algorithm for the Evaluation of Layer and Volume Potentials
Fredrik Fryklund, Leslie Greengard, Shidong Jiang +1
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory…
An FMM Accelerated Poisson Solver for Complicated Geometries in the Plane using Function Extension
Fredrik Fryklund, Leslie Greengard
We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a v…
An integral equation method for the advection-diffusion equation on time-dependent domains in the plane
Fredrik Fryklund, Sara Pålsson, Anna-Karin Tornberg
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer acc…
An accurate and efficient scheme for function extensions on smooth domains
Charles L. Epstein, Fredrik Fryklund, Shidong Jiang
A new scheme is proposed to construct an n-times differentiable function extension of an n-times differentiable function defined on a smooth domain D in d-dimensions. The extension…
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…
An integral equation based numerical method for the forced heat equation on complex domains
Fredrik Fryklund, Mary Catherine A. Kropinski, Anna-Karin Tornberg
Integral equation based numerical methods are directly applicable to homogeneous elliptic PDEs, and offer the ability to solve these with high accuracy and speed on complex domains…
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…
Partition of Unity Extension of Functions on Complex Domains
Fredrik Fryklund, Erik Lehto, Anna-Karin Tornberg
We introduce an efficient algorithm, called partition of unity extension or PUX, to construct an extension of desired regularity of a function given on a complex multiply connected…