Anna‐Karin Tornberg
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View article: A method of fundamental solutions for large-scale 3D elastance and mobility problems
A method of fundamental solutions for large-scale 3D elastance and mobility problems Open
The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here, we present new scalable MFS formul…
View article: Stabilizing the singularity swap quadrature for near-singular line integrals
Stabilizing the singularity swap quadrature for near-singular line integrals Open
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 most settings, it is known to suffer from catastrophic can…
View article: Error estimate based adaptive quadrature for layer potentials over axisymmetric surfaces
Error estimate based adaptive quadrature for layer potentials over axisymmetric surfaces Open
Layer potentials represent solutions to partial differential equations in an integral equation formulation. When numerically evaluating layer potentials at evaluation points close to the domain boundary, specialized quadrature techniques a…
View article: A Method of Fundamental Solutions for Large-Scale 3D Elastance and Mobility Problems
A Method of Fundamental Solutions for Large-Scale 3D Elastance and Mobility Problems Open
The method of fundamental solutions (MFS) is known to be effective for solving 3D Laplace and Stokes Dirichlet boundary value problems in the exterior of a large collection of simple smooth objects. Here we present new scalable MFS formula…
View article: Accurate close interactions of Stokes spheres using lubrication-adapted image systems
Accurate close interactions of Stokes spheres using lubrication-adapted image systems Open
Stokes flows with near-touching rigid particles induce near-singular lubrication forces under relative motion, making their accurate numerical treatment challenging. With the aim of controlling the accuracy with a computationally cheap met…
View article: Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology
Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology Open
Numerical simulations with rigid particles, drops, or vesicles constitute some examples that involve 3D objects with spherical topology. When the numerical method is based on boundary integral equations, the error in using a regular quadra…
View article: Fast Ewald summation for Stokes flow with arbitrary periodicity
Fast Ewald summation for Stokes flow with arbitrary periodicity Open
A fast and spectrally accurate Ewald summation method for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is presented. This work extends the previously developed Spectral Ewald method for Stok…
View article: A locally corrected multiblob method with hydrodynamically matched grids for the Stokes mobility problem
A locally corrected multiblob method with hydrodynamically matched grids for the Stokes mobility problem Open
Inexpensive numerical methods are key to enabling simulations of systems of a large number of particles of different shapes in Stokes flow and several approximate methods have been introduced for this purpose. We study the accuracy of the …
View article: Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology
Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology Open
Numerical simulations with rigid particles, drops or vesicles constitute some examples that involve 3D objects with spherical topology. When the numerical method is based on boundary integral equations, the error in using a regular quadrat…
View article: A Barrier Method for Contact Avoiding Particles in Stokes Flow
A Barrier Method for Contact Avoiding Particles in Stokes Flow Open
Rigid particles in a Stokesian fluid can physically not overlap, as a thin layer of fluid always separates a particle pair, exerting increasingly strong repulsive forces on the bodies for decreasing separations. Numerically, resolving thes…
View article: An integral equation method for the advection-diffusion equation on time-dependent domains in the plane
An integral equation method for the advection-diffusion equation on time-dependent domains in the plane Open
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
View article: Fast Ewald summation for Stokes flow with arbitrary periodicity
Fast Ewald summation for Stokes flow with arbitrary periodicity Open
A fast and spectrally accurate Ewald summation method for the evaluation of stokeslet, stresslet and rotlet potentials of three-dimensional Stokes flow is presented. This work extends the previously developed Spectral Ewald method for Stok…
View article: A Locally Corrected Multiblob Method with Hydrodynamically Matched Grids for the Stokes Mobility Problem
A Locally Corrected Multiblob Method with Hydrodynamically Matched Grids for the Stokes Mobility Problem Open
Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been introduced for this purpose. We study the accuracy of the multi…
View article: An integral equation method for the advection-diffusion equation on time-dependent domains in the plane
An integral equation method for the advection-diffusion equation on time-dependent domains in the plane Open
Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…
View article: An adaptive kernel-split quadrature method for parameter-dependent layer potentials
An adaptive kernel-split quadrature method for parameter-dependent layer potentials Open
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 dimensions. However, it can fail completely for the layer potenti…
View article: Parabolic velocity profile causes shape-selective drift of inertial ellipsoids
Parabolic velocity profile causes shape-selective drift of inertial ellipsoids Open
Understanding particle drift in suspension flows is of the highest importance in numerous engineering applications where particles need to be separated and filtered out from the suspending fluid. Commonly known drift mechanisms such as the…
View article: An adaptive kernel-split quadrature method for parameter-dependent layer potentials
An adaptive kernel-split quadrature method for parameter-dependent layer potentials Open
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 dimensions. However, it can fail completely for the layer potenti…
View article: Fast Ewald summation for electrostatic potentials with arbitrary periodicity
Fast Ewald summation for electrostatic potentials with arbitrary periodicity Open
A unified treatment for the fast and spectrally accurate evaluation of electrostatic potentials with periodic boundary conditions in any or none of the three spatial dimensions is presented. Ewald decomposition is used to split the problem…
View article: Parabolic velocity profile causes drift of inertial prolate spheroids -- but gravity is stronger
Parabolic velocity profile causes drift of inertial prolate spheroids -- but gravity is stronger Open
Motion of elongated particles in shear is studied. In applications where particles are much heavier than the carrying fluid, e.g. aerosols, the influence of particle inertia dominates the particle dynamics. Assuming that the particle only …
View article: Fast Ewald summation for electrostatic potentials with arbitrary periodicity
Fast Ewald summation for electrostatic potentials with arbitrary periodicity Open
A unified treatment for the fast and spectrally accurate evaluation of electrostatic potentials with periodic boundary conditions in any or none of the three spatial dimensions is presented. Ewald decomposition is used to split the problem…
View article: Accurate evaluation of integrals in slender-body formulations for fibers\n in viscous flow
Accurate evaluation of integrals in slender-body formulations for fibers\n in viscous flow Open
A non-local slender body approximation for slender flexible fibers in Stokes\nflow can be derived, yielding an integral equation along the center lines of\nthe fibers that involves a slenderness parameter. The formulation contains a\nso-ca…
View article: Accurate evaluation of integrals in slender-body formulations for fibers in viscous flow
Accurate evaluation of integrals in slender-body formulations for fibers in viscous flow Open
A non-local slender body approximation for slender flexible fibers in Stokes flow can be derived, yielding an integral equation along the center lines of the fibers that involves a slenderness parameter. The formulation contains a so-calle…
View article: Quadrature error estimates for layer potentials evaluated near curved surfaces in three dimensions
Quadrature error estimates for layer potentials evaluated near curved surfaces in three dimensions Open
The quadrature error associated with a regular quadrature rule for evaluation of a layer potential increases rapidly when the evaluation point approaches the surface and the integral becomes nearly singular. Error estimates are needed to d…
View article: An accurate integral equation method for Stokes flow with piecewise smooth boundaries
An accurate integral equation method for Stokes flow with piecewise smooth boundaries Open
Two-dimensional Stokes flow through a periodic channel is considered. The channel walls need only be Lipschitz continuous, in other words they are allowed to have corners. Boundary integral methods are an attractive tool for numerically so…
View article: An integral equation method for closely interacting surfactant‐covered droplets in wall‐confined Stokes flow
An integral equation method for closely interacting surfactant‐covered droplets in wall‐confined Stokes flow Open
Summary A highly accurate method for simulating surfactant‐covered droplets in two‐dimensional Stokes flow with solid boundaries is presented. The method handles both periodic channel flows of arbitrary shape and stationary solid constrict…