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 Unpublished.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.
• 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.
• Y. Zhong, K. Ren, O. Runborg and R. Tsai. Error analysis for the implicit boundary integral method. BIT, 65(8) 2025.

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