Publications
- B. Engquist and O. Runborg.
Multi-phase computations in
geometrical optics. J. Comput.
Appl. Math., 74:175-192, 1996.
- O. Runborg. Multi-phase computations in
geometrical optics. Licentiate's Thesis. TRITA-NA-9609.
NADA, KTH, 1996.
- O. Runborg. Multiscale and multiphase methods for
wave propagation. PhD Thesis. TRITA-NA-9818.
NADA, KTH, 1998.
- B. Engquist and O. Runborg.
Multiphase computations in geometrical optics.
In M. Fey and R. Jeltsch, editors, Hyperbolic Problems: Theory,
Numerics, Applications, volume 129 of Internat. Ser. Numer. Math., Zürich, Switzerland, 1998. ETH Zentrum.
- O. Runborg.
A Note on "Self-Organized Criticality: Analysis
and Simulation of a 1D Sandpile".
1998. Unpublished.
-
O. Runborg. A multiblock mesh manager.
In D. P. Hills et. al., editor, Computational Mesh Adaptation,
volume 69 of Notes on Numerical Fluid Mechanics, pages 143-162.
Vieweg, 1999.
- U. Andersson, B. Engquist, G. Ledfelt and O. Runborg.
A contribution to wavelet-based subgrid modeling.
Appl. Comput. Harmon. Anal., 7:151-164, 1999.
- O. Runborg. Some new results in multiphase geometrical optics.
M2AN Math. Model. Numer. Anal., 34:1203-1231, 2000.
- P.-O. Persson and O. Runborg.
Simulation of a waveguide filter
using wavelet-based numerical homogenization.
J. Comput. Phys., 166:361-382, 2001.
- B. Engquist and O. Runborg.
Wavelet-based numerical homogenization with applications.
In T.J. Barth, T.F. Chan and R. Haimes, editors,
Multiscale and Multiresolution Methods: Theory and Applications,
pages 97-148,
volume 20 of
Lecture Notes in Computational Science and Engineering,
Heidelberg, 2001. Springer Verlag.
- F. Castella, B. Perthame and O. Runborg.
High frequency limit of the Helmholtz equation II: Source on a
general smooth manifold. Commun. Part. Diff. Eq.,
27:607-651, 2002.
- B. Engquist, O. Runborg and A.-K. Tornberg.
High frequency wave propagation by the segment projection method.
J. Comput. Phys., 178:373-390, 2002.
- B. Engquist and O. Runborg.
Projection generated homogenization.
In N. Antonic, C. J. van Duijn, W. Jäger, and A. Mikelic,
editors, Multiscale Problems in Science and Technology,
pages 129-150, Springer-Verlag, 2002.
- O. Runborg, C. Theodoropoulos and I. G. Kevrekidis.
Effective bifurcation analysis:
a time-stepper based approach.
Nonlinearity, 15:491-511, 2002.
- I. G. Kevrekidis,
C. W. Gear,
J. M. Hyman,
P. G. Kevrekidis,
O. Runborg and C. Theodoropoulos.
Equation-free, coarse-grained multiscale computation:
enabling microscopic simulators to perform system-level tasks.
Commun. Math. Sci., 1:715-762, 2003.
- B. Engquist and O. Runborg.
Computational high frequency wave propagation.
Acta Numerica, 12:181-266, 2003.
- I. Daubechies, O. Runborg and W. Sweldens.
Normal multiresolution approximation of curves.
Constr. Approx., 20:399-463, 2004.
-
J. Krishnan,
O. Runborg and I. G. Kevrekidis,
Bifurcation analysis of nonlinear reaction-diffusion problems
using wavelet-based reduction techniques.
Comput. Chem. Eng., 28:557-574, 2004.
-
J.-D. Benamou, F. Collino and O. Runborg.
Numerical microlocal analysis of harmonic wavefields.
J. Comput. Phys., 199:717-741, 2004.
-
J. Möller, O. Runborg, P. G. Kevrekidis, K. Lust,
and I. G. Kevrekidis.
Equation-free, effective computation for discrete systems:
a time stepper based approach.
Int. J. Bifurcat. Chaos, 15:975-996, 2005.
-
L. Gosse and O. Runborg.
Finite moment problems and applications to multiphase
computations in geometric optics.
Commun. Math. Sci., 3:373-392, 2005.
-
O. Runborg.
Introduction to normal multiresolution analysis.
In B. Engquist, P. Lötstedt, O. Runborg, editors,
Multiscale Methods in Science and Engineering,
pages 205-224,
volume 44 of
Lecture Notes in Computational Science and Engineering,
Heidelberg, 2005. Springer Verlag.
-
L. Gosse and O. Runborg.
Resolution of the finite Markov moment problem.
C. R. Math. Acad. Sci. Paris, Ser I 341:775-780, 2005.
-
M. Motamed and O. Runborg.
A fast phase space method for computing creeping rays.
J. Comput. Phys., 219:276-295, 2006.
-
O. Runborg
Mathematical models and numerical methods for
high frequency waves.
Commun. Comput. Phys., 2:827-880, 2007.
-
I. Daubechies, O. Runborg and J. Zou.
A sparse spectral method for homogenization multiscale problems.
Multiscale Model. Sim., 6(3):711-740, 2007.
-
M. Motamed and O. Runborg.
A multiple-patch phase space method for computing
trajectories on manifolds with applications to wave
propagation problems.
Commun. Math. Sci., 5(3):617-648, 2007.
-
L. Gosse and O. Runborg.
Existence, uniqueness, and a constructive solution algorithm for a class of finite Markov moment problems.
SIAM J. Appl. Math. 68(6):1618-1640, 2008.
-
O. Runborg.
Fast interface tracking via a multiresolution
representation of curves and surfaces.
Commun. Math. Sci., 7(2):365-398, 2009.
-
M. Motamed and O. Runborg.
Taylor expansion and discretization errors in Gaussian beam superposition.
Wave Motion, 47(7):421-439, 2010.
-
B. Engquist, H. Holst and O. Runborg.
Multi-scale methods for wave
propagation in heterogeneous media.
Commun. Math. Sci., 9(1):33-56, 2011.
-
J. Popovic and O. Runborg.
Analysis of a fast method for solving the high frequency
Helmholtz equation in one dimension.
BIT, 51(3):721-755, 2011.
-
B. Engquist, H. Holst and O. Runborg.
Multiscale methods for wave propagation
in heterogeneous media over long time.
In B. Engquist, O. Runborg, Y.-H. R. Tsai, editors,
Numerical Analysis of Multiscale Computations,
pages 167-186,
volume 82 of
Lecture Notes in Computational Science and Engineering,
Heidelberg, 2011. Springer Verlag.
-
B. Engquist, H. Holst and O. Runborg.
Analysis of HMM for one dimensional wave propagation problems over long time.
arXiv:1111.2541v1, 2011.
-
B. Engquist, J. Häggblad and O. Runborg.
On energy preserving consistent boundary condtitions for the Yee scheme in 2D.
BIT 52(3):615--637, 2012.
-
H. Liu, O. Runborg and N. M. Tanushev.
Error estimates for Gaussian beam superpositions.
Math. Comp. 82:919-952, 2013.
-
O. Runborg.
Analysis of high order fast interface tracking methods.
Numer. Math. 128(2):339-375, 2014.
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H. Liu, J. Ralston, O. Runborg and N. M. Tanushev.
Gaussian beam methods for the Helmholtz equation.
SIAM J. Appl. Math. 74(3):771-793, 2014.
-
O. Marin, O. Runborg and A.-K. Tornberg.
Corrected trapezoidal rules for a class of singular functions.
IMA J. Numer. Anal. 34(4):1509-1540, 2014.
-
J. Häggblad and O. Runborg.
Accuracy of staircase approximations in finite-difference
methods for wave propagation.
Numer. Math., 128(4):741-771, 2014.
-
D. Arjmand and O. Runborg.
Analysis of heterogeneous multiscale methods for long time wave propagation problems.
Multiscale Model. Sim., 12(3):1135-1166, 2014.
-
M. Motamed and O. Runborg.
A wavefront-based Gaussian
beam
method for computing high frequency wave propagation problems.
Comput. Math. Appl., 69(9):949-963, 2015.
-
E. Kieri, G. Kreiss and O. Runborg.
Coupling of Gaussian beam and finite difference solvers for semiclassical
Schrödinger equations.
Adv. Appl. Math. Mech., 7(6):687-714, 2015.
-
D. Arjmand and O. Runborg.
A time dependent approach for removing the cell
boundary error in elliptic homogenization problems.
J. Comput. Phys.,
314:206-227, 2016.
- H. Liu, O. Runborg and N. Tanushev.
Sobolev and max norm error estimates for Gaussian beam superpositions.
Commun. Math. Sci., 14(7):2037-2072, 2016.
- G. Malenová, M. Motamed, O. Runborg and R. Tempone.
A sparse stochastic collocation technique for high-frequency wave propagation with uncertainty.
SIAM J. Uncertainty Quantification, 4:1084-1110, 2016.
- G. Malenová, M. Motamed and O. Runborg.
Stochastic regularity of a quadratic observable of high frequency waves.
Res. Math. Sci., 4(1):1-23, 2017.
- D. Arjmand and O. Runborg.
Estimates for the upscaling error in heterogeneous multiscale
methods for wave propagation problems in locally periodic media.
Multiscale Model. Sim., 15(2):948-976, 2017.
- E. Jarlebring, G. Mele and O. Runborg.
The waveguide eigenvalue problem and the tensor infinite Arnoldi method.
SIAM J. Sci. Comput., 39(3):A1062-A1088, 2017.
- J. Popovic and O. Runborg.
Adaptive fast interface tracking methods.
J. Comput. Phys., 337(C):42-61, 2017.
- G. Malenová and O. Runborg.
Stochastic regularity of general quadratic observables of high frequency waves.
Submitted, 2019.
- D. Appelö, F. Garcia and O. Runborg.
WaveHoltz: Iterative solution of the Helmholtz equation via the wave equation.
SIAM J. Sci. Comput., 42(4):A1950-1983, 2020.
- L. Leitenmaier and O. Runborg.
On
homogenization of Landau-Lifshitz equation
with rapidly oscillating material coefficient.
Commun. Sci. Math., 20(3):653-694, 2022.
- L. Leitenmaier and O. Runborg.
Upscaling errors in heterogeneous multiscale methods for the Landau-Lifshitz equation.
Multiscale Model. Sim., 20(3):653-694, 2022.
- F. Izzo, O. Runborg and R. Tsai.
Corrected trapezoidal rules for singular implicit boundary integrals.
Accepted in
J. Comput. Phys., 2022.
- L. Leitenmaier and O. Runborg.
Heterogeneous multiscale methods for the Landau-Lifshitz equation.
SIAM J. Sci. Comput., 93, 76, 2022.
- D. Appelö, F. Garcia. A. A. Loya and O. Runborg.
El-WaveHoltz: A time-domain iterative solver for time-harmonic elastic waves.
Accepted in
Comput. Methods Appl. Mech. Eng., 2022.
- O. Lafitte and O. Runborg.
Error estimates for Gaussian beams at a fold caustic.
Accepted in
Asymptotic Anal., 2023.
- F. Izzo, O. Runborg and R. Tsai.
High-order corrected trapezoidal rules for a class of singular integrals.
Accepted in
Adv. Comput. Math., 2023.
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