Research

Description of research projects will come soon.

Publications (most recent first):

Submitted/ to be submitted:

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

S. Engblom, M. Do-Quang, G. Amberg, A.-K. Tornberg.
On modeling and simulation of surfactants in diffuse interface flow. Available on arxiv.org.

O. Marin, O. Runborg and A.-K. Tornberg.
Corrected trapezoidal rules for a class of singular functions.

O. Marin, K. Gustavsson and A.-K. Tornberg.
A highly accurate boundary treatment for confined Stokes flow.

Published:

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.

Interface tracking methods

Spectrally accurate FFT based fast Ewald methods for Stokes flow and electrostatics.


Rigid fiber suspensions and interaction of fibers and rigid walls.


Dynamics of multiple interacting flexible fibers in Stokes flow




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