Publications

Submitted/ to be submitted:

Published (and a few reports):

A. Broms and A.-K. Tornberg.
A Barrier Method for Contact Avoiding Particles in Stokes Flow. J Comput Phys, 2024:112648. Open access.

Joar Bagge and A.-K. Tornberg.
Fast Ewald summation for Stokes flow with arbitrary periodicity. J Comput Phys, 2023:112473. Open access.

C. Sorgentone and A.-K. Tornberg.
Estimation of quadrature errors for layer potentials evaluated near surfaces with spherical topology. Adv Comput Math, 49:87, 2023. Open access

A. Broms, M. Sandberg and A.-K. Tornberg.
A Locally Corrected Multiblob Method with Hydrodynamically Matched Grids for the Stokes Mobility Problem. J Comput Phys, 2023:112172. Open access. 

F. Fryklund, S. Pålsson and A.-K. Tornberg.
An integral equation method for the advection-diffusion equation on time-dependent domains in the plane. J Comput Phys, 2023:111856. Open access. 

L. af Klinteberg, C. Sorgentone and A.-K. Tornberg.
Quadrature error estimates for layer potentials evaluated near curved surfaces in three dimensions. Computers and Mathematics with Applications, 11:1-19, 2022. Open access.

L. af Klinteberg, F. Fryklund and A.-K. Tornberg.
An adaptive kernel-split quadrature method for parameter dependent layer potentials.
Adv Comput Math, 48:1-27, 2022. Open access

J. Bagge, T. Rosén, F. Lundell, and A.-K. Tornberg. Parabolic velocity profile causes shape-selective drift of inertial ellipsoids. J Fluid Mech, 2021. Open access https://doi.org/10.1017/jfm.2021.716

D. Saffar Shamshirgar, J. Bagge and A.-K. Tornberg.
Fast Ewald summation for electrostatic potentials with arbitrary periodicity.
J. Chem. Phys. 154, 164109 (2021). Open access https://doi.org/10.1063/5.0044895.

Joar Bagge and Anna-Karin Tornberg.
Highly accurate special quadrature methods for Stokesian particle suspensions in confined geometries. 
Int. J. Num. Meth. Fluids., 2021. Open access https://doi.org/10.1002/fld.4970

A.-K. Tornberg. Accurate evaluation of integrals in slender-body formulations for fibers in viscous flow. Available on ArXiv.org (Dec 2020). 

L. Bystricky, S. Pålsson and A.-K. Tornberg.
An accurate integral equation method for Stokes flow with piecewise smooth boundaries.
BIT Numerical Mathematics, 2021. DOI: 10.1007/s10543-020-00816-1. Open access  https://doi.org/10.1007/s10543-020-00816-1.

S. Pålsson and A.-K. Tornberg.
An integral equation method for closely interacting surfactant-covered droplets in wall-confined Stokes flow.
Int. J. Numer. Meth. Fluids, 2020. DOI 10.1002/fld.4857. Open access https://doi.org/10.1002/fld.4857. 

F. Fryklund, M. Kropinski, and A.-K. Tornberg.
An integral equation based numerical method for the forced heat equation on complex domains.
Adv Comput Math, 46:69, 2020. Open access https://doi.org/10.1007/s10444-020-09804-z.

S. Pålsson and A.-K. Tornberg.
Spectrally accurate Ewald summation for the Yukawa potential in two dimensions.
Available on ArXiv.org (Nov 2019).

D. S. Shamshirgar, R. Yokota, A.-K. Tornberg and B. Hess.
Regularizing the fast multipole method for use in molecular simulation.
J. Chem. Phys. 151:234113, 2019. Open access  https://doi.org/10.1063/1.5122859

C. Sorgenone, A-K Tornberg and P. M. Vlahovska.
A 3D boundary integral method for the electrohydrodynamics of surfactant-covered drops.
J. Comput. Phys., 389:111-127, 2019. Also available on Arxiv.org.

S. Pålsson, M. Siegel and A.-K. Tornberg.
Simulation and validation of surfactant-laden drops in two-dimensional Stokes flow.
J. Comput. Phys., 386:218-247, 2019.  Also available on Arxiv.org.

F. Fryklund and E. Lehto and A.-K. Tornberg.
Partition of unity extension on complex domains.
J. Comput. Phys., 375:57-79, 2018. Also available on Arxiv.org.

S. Srinivasan and A.-K. Tornberg.
Fast Ewald summation for Green's functions of Stokes flow in a half-space.
Res Math Sci, 5:35, 2018. Also available on Arxiv.org.

M. Siegel and A.-K. Tornberg.
A local target specific quadrature by expansion method for evaluation of layer potentials in 3D.
J. Comput. Phys., 364:365-392, 2018. Also available on Arxiv.org.

L. af Klinteberg and A.-K. Tornberg.
Adaptive Quadrature by Expansion for layer potential evaluation in two dimensions.
SIAM J. Sci. Comput, 40:A1225-A1249, 2018. Available on Arxiv.org.

C. Sorgentone and A.-K. Tornberg.
A highly accurate boundary integral equation method for surfactant-laden drops in 3D.
J. Comput. Phys., 360:167-191, 2018. Also available on Arxiv.org.

D. Saffar Shamshirgar and A.-K. Tornberg.
The spectral Ewald method for singly periodic domains.
J. Comput. Phys., 347:341-366, 2017. Also available on Arxiv.org

L. af Klinteberg, D. Saffar Shamshirgar and A.-K. Tornberg.
Fast Ewald summation for free-space Stokes potentials.
Res Math Sci, 4:1, 2017. Also available on Arxiv.org.

L. af Klinteberg and A.-K. Tornberg.
Error estimation for quadrature by expansion in layer potential evaluation.
Adv Comput Math, 43:195-234, 2017. Also available on Arxiv.org. arxiv.org

L. af Klinteberg and A.-K. Tornberg.
A fast integral equation method for solid particles in viscous flow using quadrature by expansion. J. Comput. Phys., 326:420-445, 2016. Also available on arxiv.org

A.-K. Tornberg.
The Ewald sums for singly, doubly and triply periodic elecrostatic systems. Advances in computational mathematics, 42:227-248, 2016.
Available on arxiv.org.

R. Ojala and A.-K. Tornberg. An accurate integral equation method for simulating multi-phase Stokes flow. J. Comput. Phys. 298:145-160, 2015.

L. af Klinteberg and A.-K. Tornberg. Fast Ewald summation for Stokesian particle suspensions. Int. J. Num. Meth. Fluids. 76:669-698, 2014.

L. af Klinteberg, D. Lindbo and A.-K. Tornberg. An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant. Comput Fluids, 101:50-63, 2014.

S. Khatri and A.-K. Tornberg.
An embedded boundary method for soluble surfactants with intefrca tracking for two-phase flows. J. Comput. Phys. . 256:768-790, 2014.

O. Marin, O. Runborg and A.-K. Tornberg.
Corrected trapezoidal rules for a class of singular functions.
IMA J. Num. Analys. 2013. doi: 10.1093/imanum/drt046

S. Engblom, M. Do-Quang, G. Amberg, A.-K. Tornberg.
On modeling and simulation of surfactants in diffuse interface flow. Commun. Comput. Phys. 14:879-915, 2013.

O. Marin, K. Gustavsson and A.-K. Tornberg.
A highly accurate boundary treatment for confined Stokes flow.
Comput. Fluids. . 66:215-230, 2012.

D. Lindbo and A.-K. Tornberg.
Fast and spectrally accurate Ewald summation of 2-periodic Stokes potentials.
Available on Arxiv.org.

D. Lindbo and A.-K. Tornberg.
Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems. J. Chem. Phys. 136:164111, 2012, doi: 10.1063/1.4704177

D. Lindbo and A.-K. Tornberg.
Spectral accuracy in fast Ewald-based methods for particle simulations. J. Comput. Phys. 2011, doi:10.1016/j.jcp.2011.08.022

S. Khatri S and A.-K. Tornberg.
A numerical method for two phase flows with insoluble surfactants. Comput. Fluids. 49:150-165, 2011.

D. Lindbo and A.-K. Tornberg.
Spectrally accurate fast summation for periodic Stokes potentials. J. Comput. Phys. 229:8994-9010, 2010.

S. Zahedi and A.-K. Tornberg.
Delta function approximations in level set methods by distance function extension. J. Comput. Phys. 229:2199-2219, 2010.

A. Kanevsky and M.J. Shelley and A.-K. Tornberg.
Modeling simple locomotors in Stokes flow. J. Comput. Phys. 229:958-977, 2010.

K. Gustavsson and A.-K. Tornberg.
Gravity induced sedimentation of slender fibers Phys. Fluids. 21: 123301, 2009.

A.-K. Tornberg and B. Engquist.
Consistent boundary conditions for the Yee scheme.A J. Comput. Phys. 227:6922-6943, 2008.

A.-K. Tornberg and L. Greengard.
A fast multipole method for the three-dimensional Stokes equations. J. Comput. Phys. 227:1613-1619, 2008.

A.-K. Tornberg and B. Engquist.
Regularization for accurate numerical wave propagation in discontinuous media. Meth. Appl. Anal. 13: 247-274, 2006.

A.-K. Tornberg, B. Engquist, B. Gustafsson and P. Wahlund.
A new type of boundary treatment for wave propagation. BIT . 46:s145-s170, 2006.

S. Jung, S.E. Spagnolie, K. Parikh, M.J. Shelley and A-K. Tornberg.
Periodic Sedimentation in a Stokesian Fluid. Physical Review E. 74:035302, 2006.

A.-K. Tornberg and K. Gustavsson.
A numerical method for simulations of rigid fiber suspensions. J. Comput. Phys. 215:172-196, 2006.

A.-K. Tornberg.
Regularization techniques for singular source terms in differential equations.
In Laptev, A. (ed.), European Congress of Mathematics (ECM), Stockholm, Sweden, June 27-July 2, 2004. Zurich: European Mathematical Society (2005). (ISBN 3-03719-009-4, pages 477-499).

B. Engquist, A.-K. Tornberg and R. Tsai.
Discretization of Dirac Delta Functions in Level Set Methods.
J. Comput. Phys. 207:28-51, 2005.

A.-K. Tornberg.
Numerical Simulations of the Dynamics of Fiber Suspensions.
In Multiscale methods in Science and Engineering (Lecture Notes in Computational Science and Engineering) , editors B. Engquist et al., Springer-Verlag, 2005 (ISBN 3540253351).

M.J. Shelley and A.-K. Tornberg.
Microstructural Dynamics in Complex Fluids.
In the chapter on Mathematical Methods (editor M. Bazant) in Handbook of Materials Modeling .
Kluwer Academic Publishers, 2005 (ISBN 1402032870).

A.-K. Tornberg and B. Engquist.
Numerical approximations of singular source terms in differential equations.
J. Comput. Phys. 200:462-488, 2004.

A.-K. Tornberg and M.J, Shelley.
Simulating the Dynamics and Interactions of Flexible Fibers in Stokes Flows.
J. Comput. Phys. 196:8-40, 2004.

A.-K. Tornberg and B. Engquist.
Regularization Techniques for Numerical Approximation of PDEs with Singularities.
Journal of Scientific Computing . 19:527-552, 2003.

A.-K. Tornberg and B. Engquist.
The Segment Projection Method for Interface Tracking.
Commun. Pur. Appl. Math. , 56:47-79, 2003.

B. Engquist, O. Runborg and A.-K. Tornberg.
The Segment Projection Method for Geometrical Optics.
J. Comput. Phys. 178:373:390, 2002.

A.-K. Tornberg.
Multi-Dimensional Quadrature of Singular and Discontinuous Functions.
BIT . 42:644-669, 2002.

A.-K. Tornberg and B. Engquist.
Interface Tracking in Two-Phase Flows.
Multifield Problems, State of the Art , Springer Verlag, Berlin, 58-66, 2000.

A.-K. Tornberg.
Interface Tracking Methods with Application to Multiphase Flows. (This file is huge).
PhD Thesis , NADA, KTH, Stockholm, Sweden, 2000. ISBN 91-7170-558-9, TRITA-NA 0010.

A.-K. Tornberg and B. Engquist.
Finite Element Based Methods for Interfacial Flow Simulations.
Finite Element Based Methods for Interfacial Flow Simulations. Proceedings of ENUMATH99,
World Scientific Publ. 251-258, 2000.

A.-K. Tornberg and B. Engquist.
A Finite Element Based Level Set Method for Multiphase Flow Applications.
Computing and Visualization in Science, 3:93-101, 2000.

A.-K. Tornberg.
A Finite Element Based Level Set Method for Multiphase Flow Simulations.
Licentiate's Thesis , NADA, KTH, Stockholm, Sweden, 1998. ISBN 91-7170-317-9, TRITA-NA-9817.

A.-K. Tornberg, R. W. Metcalfe, R. Scott, and B. Bagheri.
A Fluid Particle Simulation Method
In Computational Science for the 21st century (M-O. Bristeau et al., eds.). John Wiley & Sons, New York, pp 312-321 (1997).

A.-K. Tornberg, R. W. Metcalfe, R. Scott, and B. Bagheri.
A Front-Tracking Method for Simulating Fluid Particle Motion using High-Order Finite Element Methods.
1997 ASME Fluids Engineering Division Summer Meeting FEDSM97-3493.