lrAA: Low-Rank Anderson Acceleration
D. Appelö and Y. Cheng. SIAM Journal on Scientific Computing, 48(4):A1925-A1950, 2026.
Publications
Journal Articles
Convergence of the semi-discrete WaveHoltz iteration
A. Rotem, O. Runborg and D. Appelö. Journal of Computational Physics, 558:114882, 2026.
LR-WaveHoltz: A low-rank Helmholtz solver
A. Granath, D. Appelö and S. Wang. Journal of Computational Physics, page 115175, 2026.
EigenWave: An optimal O(N) method for computing eigenvalues and eigenvectors by time-filtering the wave equation
D. Appelö, J. W. Banks, W. D. Henshaw, N. Le and D. W. Schwendeman. Journal of Computational Physics, page 114758, 2026.
An O(N) Helmholtz solver using WaveHoltz and overset grids
D. Appelö, J. W. Banks, W. D. Henshaw and D. W. Schwendeman. SIAM Journal on Scientific Computing, 48(3):A1367-A1398, 2026.
A rule of thumb for choosing points-per-wavelength for finite difference approximations of Helmholtz problems
D. Appelö, J. W. Banks, W. D. Henshaw and D. W. Schwendeman. Journal of Computational Physics, page 114703, 2026.
High-order Hermite optimization: Fast and exact gradient computation in open-loop quantum optimal control using a discrete adjoint approach
S. Lee and D. Appelö. Journal of Computational Physics, 552:114697, 2026.
Fast and high-order approximation of parabolic equations using hierarchical direct solvers and implicit Runge-Kutta methods
K. Chen, D. Appelö, T. Babb and P.-G. Martinsson. Communications on Applied Mathematics and Computation, 8(1):248-268, 2026.
Preconditioning low rank generalized minimal residual method (GMRES) for implicit discretizations of matrix differential equations
S. Meng, D. Appelö and Y. Cheng. SIAM Journal on Matrix Analysis and Applications, 46(4):2475-2500, 2025.
Kraus is King: High-order completely positive and trace preserving (CPTP) low rank method for the Lindblad master equation
D. Appelö and Y. Cheng. Journal of Computational Physics, 534:114036, 2025.
The Hermite-Taylor correction function method for embedded boundary and Maxwell’s interface problems
Y.-M. Law, D. Appelö and T. Hagstrom. Journal of Computational Physics, 537(3):114111, 2025.
Energy-conserving Hermite methods for Maxwell’s equations
D. Appelö, T. Hagstrom and Y.-M. Law-Kam-Cio. Communications on Applied Mathematics and Computation, 7:1146-1173, 2025.
Robust implicit adaptive low rank time-stepping methods for matrix differential equations
D. Appelö and Y. Cheng. Journal of Scientific Computing, 102(3):81, 2025.
High order accurate Hermite schemes on curvilinear grids with compatibility boundary conditions
A. Alvarez Loya, D. Appelö and W. D. Henshaw. Journal of Computational Physics, 522:113597, 2025.
The Hermite-Taylor correction function method for Maxwell’s equations
Y.-M. Law and D. Appelö. Communications on Applied Mathematics and Computation, 2023.
Universal AMG accelerated embedded boundary method without small cell stiffness
Z. Peng, D. Appelö and S. Liu. Journal of Scientific Computing, 97(2):40, 2023.
Noise-specific beating in the higher-level Ramsey curves of a transmon qubit
L. A. Martinez, Z. Peng, D. Appelö, D. M. Tennant, N. Anders Petersson, J. L. DuBois and Y. J. Rosen. Applied Physics Letters, 122(11):114002, 2023.
An energy-based discontinuous Galerkin method with tame CFL numbers for the wave equation
D. Appelö, L. Zhang, T. Hagstrom and F. Li. BIT Numerical Mathematics, 63(1):5, 2023.
Fourier continuation discontinuous Galerkin methods for linear hyperbolic problems
D. Appelö, K. van der Sande and N. Albin. Communications on Applied Mathematics and Computation, 5:1385-1405, 2023.
El-WaveHoltz: A time-domain iterative solver for time-harmonic elastic waves
D. Appelö, F. Garcia, A. Alvarez Loya and O. Runborg. Computer Methods in Applied Mechanics and Engineering, 401:115603, 2022.
EM-WaveHoltz: A flexible frequency-domain method built from time-domain solvers
Z. Peng and D. Appelö. IEEE Transactions on Antennas and Propagation, 70(7):5659-5671, 2022.
An energy-based summation-by-parts finite difference method for the wave equation in second order form
S. Wang, D. Appelö and G. Kreiss. Journal of Scientific Computing, 91(2):1-22, 2022.
Anderson acceleration based on the Hs Sobolev norm for contractive and noncontractive fixed-point operators
Y. Yang, A. Townsend and D. Appelö. Journal of Computational and Applied Mathematics, 403:113844, 2022.
Accuracy of spectral element method for wave, parabolic, and Schrodinger equations
H. Li, D. Appelö and X. Zhang. SIAM Journal on Numerical Analysis, 60(1):339-363, 2022.
A Hermite method with a discontinuity sensor for Hamilton-Jacobi equations
A. Alvarez Loya and D. Appelö. Journal of Scientific Computing, 90(3):1-31, 2022.
Energy-based discontinuous Galerkin difference methods for second-order wave equations
L. Zhang, D. Appelö and T. Hagstrom. Communications on Applied Mathematics and Computation, pages 1-25, 2021.
WaveHoltz: Iterative solution of the Helmholtz equation via the wave equation
D. Appelö, F. Garcia and O. Runborg. SIAM Journal on Scientific Computing, 42(4):A1950-A1983, 2020.
An energy-based discontinuous Galerkin method for semilinear wave equations
D. Appelö, T. Hagstrom, Q. Wang and L. Zhang. Journal of Computational Physics, 418:109608, 2020.
Hermite-discontinuous Galerkin overset grid methods for the scalar wave equation
O. Beznosov and D. Appelö. Communications on Applied Mathematics and Computation, 2020.
Reevaluation of spin-orbit dynamics of polarized e-e+ beams in high energy circular accelerators and storage rings: An approach based on a Bloch equation
K. Heinemann, D. Appelö, D. P. Barber, O. Beznosov and J. A. Ellison. International Journal of Modern Physics A, 35(15n16):2041003, 2020.
The Bloch equation for spin dynamics in electron storage rings: Computational and theoretical aspects
K. Heinemann, D. Appelö, D. P. Barber, O. Beznosov and J. A. Ellison. International Journal of Modern Physics A, 34(36):1942032, 2019.
Energy stable SBP-FDTD methods for Maxwell-Duffing models in nonlinear photonics
D. Appelö, V. A. Bokil, Y. Cheng and F. Li. IEEE Journal on Multiscale and Multiphysics Computational Techniques, 4:329-336, 2019.
Wasserstein metric-driven Bayesian inversion with application to wave propagation problems
M. Motamed and D. Appelö. International Journal for Uncertainty Quantification, 9(4):395-414, 2019.
An energy-based discontinuous Galerkin method for the wave equation with advection
L. Zhang, T. Hagstrom and D. Appelö. SIAM Journal of Numerical Analysis, 57(5):2469-2492, 2019.
An energy-based discontinuous Galerkin method for coupled elasto-acoustic wave equations in second-order form
D. Appelö and S. Wang. International Journal for Numerical Methods in Engineering, 119(7):618-638, 2019.
Hermite methods for the scalar wave equation
D. Appelö, T. Hagstrom and A. Vargas. SIAM Journal on Scientific Computing, 40(6):A3902-A3927, 2018.
Flux-conservative Hermite methods for simulation of nonlinear conservation laws with shocks
A. Kornelus and D. Appelö. Journal of Scientific Computing, 76:24-47, 2018.
A MultiOrder discontinuous Galerkin Monte Carlo method for hyperbolic problems with stochastic parameters
M. Motamed and D. Appelö. SIAM Journal on Numerical Analysis, 56(1):448-468, 2018.
An energy-based discontinuous Galerkin discretization of the elastic wave equation in second order form
D. Appelö and T. Hagstrom. Computer Methods in Applied Mechanics and Engineering, 338:362-391, 2018.
An explicit Hermite-Taylor method for the Schrodinger equation
D. Appelö, G. Kreiss and S. Wang. Communications in Computational Physics, 21(5):1207-1230, 2017.
A new discontinuous Galerkin formulation for wave equations in second order form
D. Appelö and T. Hagstrom. SIAM Journal on Numerical Analysis, 53(6):2705-2726, 2015.
A hybrid Hermite-discontinuous Galerkin method for hyperbolic systems with application to Maxwell’s equations
X. Chen, D. Appelö and T. Hagstrom. Journal of Computational Physics, 257, Part A:501-520, 2014.
A fourth-order embedded boundary method for the wave equation
D. Appelö and N. A. Petersson. SIAM Journal on Scientific Computing, 34(6):2982-3008, 2012.
Numerical methods for solid mechanics on overlapping grids: Linear elasticity
D. Appelö, J. W. Banks, W. D. Henshaw and D. W. Schwendeman. Journal of Computational Physics, 231(18):6012-6050, 2012.
Simulation of compressible flows using Hermite methods
T. Hagstrom, D. Appelö, T. Colonius, M. Inkman and C. Y. Jang. The Journal of the Acoustical Society of America, 131(4):3429-3429, 2012.
On advection by Hermite methods
D. Appelö and T. Hagstrom. Pacific Journal of Applied Mathematics, 4(2):125-139, 2011.
Minimum energy path to membrane pore formation and rupture
C. L. Ting, D. Appelö and Z. G. Wang. Physical Review Letters, 106(16):168101, 2011.
Computational modeling and experiments of natural convection for a Titan Montgolfiere
A. Samanta, D. Appelö, T. Colonius, J. Nott and J. Hall. AIAA Journal, 5:1007-1016, 2010.
A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems
D. Appelö and T. Colonius. Journal of Computational Physics, 228(11):4200-4217, 2009.
A stable finite difference method for the elastic wave equation on complex geometries with free surfaces
D. Appelö and N. A. Petersson. Communications in Computational Physics, 5(1):84-107, 2009.
A general perfectly matched layer model for hyperbolic-parabolic systems
D. Appelö and T. Hagstrom. SIAM Journal on Scientific Computing, 31(5):3301-3323, 2009.
On cylindrically converging shock waves shaped by obstacles
V. Eliasson, W. D. Henshaw and D. Appelö. Physica D: Nonlinear Phenomena, 237(14-17):2203-2209, 2008.
Application of a perfectly matched layer to the nonlinear wave equation
D. Appelö and G. Kreiss. Wave Motion, 44(7-8):531-548, 2007.
Automatic symmetrization and energy estimates using local operators for partial differential equations
T. Hagstrom and D. Appelö. Communications in Partial Differential Equations, 32(7):1129-1145, 2007.
Perfectly matched layers for hyperbolic systems: General formulation, well-posedness, and stability
D. Appelö, T. Hagstrom and G. Kreiss. SIAM Journal on Applied Mathematics, 67(1):1-23, 2006.
A new absorbing layer for elastic waves
D. Appelö and G. Kreiss. Journal of Computational Physics, 215(2):642-660, 2006.
Preprints and Submitted Manuscripts
Filon methods for highly oscillatory controlled quantum systems
S. Lee and D. Appelö. Submitted to SIAM Journal on Scientific Computing, Special Section on Quantum Computing: Numerical Algorithms and Applications, 2026.
Gregory nested Picard iteration schemes for open quantum systems governed by the Lindblad equation
J. Hu, D. Appelö and Y. Cheng. arXiv:2606.29002, 2026.
Numerical study of eigenvector deflation to accelerate the WaveHoltz method
D. Appelö, W. D. Henshaw and Z. Peng. arXiv:2606.31842, 2026.
The WaveHoltz heterogeneous multiscale method
A. Rotem, O. Runborg and D. Appelö. arXiv:2607.05811, 2026.
Completely positive and trace preserving schemes with tensor train compression for the Lindblad equation
P. DelMastro, D. Appelö and Y. Cheng. arXiv:2605.01494, 2026.
Arbitrary high order low-rank completely positive and trace preserving (CPTP) schemes for Lindblad equations with time-dependent Hamiltonian
J. Hu, D. Appelö and Y. Cheng. arXiv:2511.12012, 2025.
A new cross approximation for Tucker tensors and its application in Tucker-Anderson acceleration
D. Appelö and Y. Cheng. Submitted, arXiv:2509.18554, 2025.
A multi-frequency Helmholtz solver based on the WaveHoltz algorithm
D. Appelö, F. Appiah, J. W. Banks, C. Carrick, W. D. Henshaw and D. W. Schwendeman. Submitted, arXiv:2507.23613, 2025.
A P-adaptive Hermite method for nonlinear dispersive Maxwell’s equations
Y.-M. Law, Z. Peng, D. Appelö and T. Hagstrom. arXiv:2504.09269, 2025.
Deterministic and Bayesian characterization of quantum computing devices
Z. Peng, D. Appelö, N. A. Petersson, M. Motamed, F. Garcia and Y. Cho. arXiv:2306.13747, 2024.
Book Chapters
On the scaling of entropy viscosity in high order methods
A. Kornelus and D. Appelö. In Springer Lecture Notes in Computational Science and Engineering: ICOSAHOM 2016, Rio de Janeiro, pages 175-187. Springer, 2017.
Simulation and modeling of turbulent jet noise
T. Colonius, A. Sinha, D. Rodriguez, A. Towne, J. Liu, G. A. Bres, D. Appelö and T. Hagstrom. In Direct and Large-Eddy Simulation IX, ERCOFTAC Series, pages 305-310. Springer International Publishing, 2015.
Solving PDEs with Hermite interpolation
T. Hagstrom and D. Appelö. In Springer Lecture Notes in Computational Science and Engineering: ICOSAHOM 2014, Salt Lake City, pages 31-49. Springer, 2015.
Conference and Proceedings Papers
WaveHoltz: Parallel and scalable solution of the Helmholtz equation
D. Appelö, F. Garcia and O. Runborg. Pages 1541-1545, 2019.
Energy stable staggered high order finite differences for optical media
D. Appelö, V. Bokil, Y. Cheng and F. Li. In 2019 International Applied Computational Electromagnetics Society Symposium (ACES), pages 1-2, April 2019.
HPS accelerated spectral solvers for time dependent problems: Part 1, algorithms
T. Babb, P.-G. Martinsson and D. Appelö. In Proceedings of Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2018.
HPS accelerated spectral solvers for time dependent problems: Part 2, numerical experiments
T. Babb, P.-G. Martinsson and D. Appelö. In Proceedings of Spectral and High Order Methods for Partial Differential Equations, ICOSAHOM 2018.
A pseudospectral method for solving the Bloch equations of the polarization density in e- storage rings
A. Klaus, O. Beznosov, J. A. Ellison, D. P. Barber and D. Appelö. In 9th International Particle Accelerator Conference, IPAC2018, Vancouver, BC, Canada, 2018.
An analysis of dispersion and dissipation properties of Hermite methods and its application to direct numerical simulation of jet noise
C. Y. Jang, D. Appelö, T. Colonius, T. Hagstrom and M. Inkman. In 18th AIAA/CEAS Aeroacoustics Conference (33rd AIAA Aeroacoustics Conference), 2012.
Hermite methods for aeroacoustics: Recent progress
D. Appelö, M. Inkman, T. Hagstrom and T. Colonius. In 17th AIAA/CEAS Aeroacoustics Conference, Portland, Oregon, number AIAA-2011-2757, 2011.
Development of arbitrary-order Hermite methods for simulation and analysis of turbulent jet noise
D. Appelö, T. Colonius, T. Hagstrom and M. Inkman. Procedia Engineering: IUTAM Symposium on Computational Aero-Acoustics for Aircraft Noise Prediction, University of Southampton, 2010.
Computational modeling and experiments of natural convection for a Titan Montgolfiere
T. Colonius, D. Appelö, J. Nott and J. Hall. In AIAA Balloon Systems Conference, AIAA-2009-2806, Seattle, 2009.
Experiments with Hermite methods for simulating compressible flows: Runge-Kutta time-stepping and absorbing layers
T. Hagstrom and D. Appelö. In 13th AIAA/CEAS Aeroacoustics Conference, number 2007-3505, 2007.
Construction of stable PMLs for general 2x2 symmetric hyperbolic systems
D. Appelö and T. Hagstrom. In Proceedings of the Tenth International Conference on Hyperbolic Problems: Theory, Numerics, Applications, Osaka, 2004.
Evaluation of a well-posed perfectly matched layer for computational acoustics
D. Appelö and G. Kreiss. In E. Tadmor and T. Y. Hou, editors, Hyperbolic Problems: Theory, Numerics, Applications, pages 285-294. Springer Verlag, 2002.
Extended Abstracts
An energy based discontinuous Galerkin method for acoustic-elastic waves
D. Appelö and S. Wang. Extended abstract, Waves 2017.
An energy based discontinuous Galerkin method for Hamiltonian systems
D. Appelö, T. Hagstrom and A. Semenova. Extended abstract, Waves 2017.
Sobolev-dG: A class of dG methods with tame CFL numbers
D. Appelö, T. Hagstrom and A. Kornelus. Extended abstract, Waves 2017.
A new discontinuous Galerkin formulation for wave equations in second order form
D. Appelö and T. Hagstrom. Extended abstract, Waves 2015.
Application of the entropy viscosity method to Hermite methods for shock problems
A. Kornelus and D. Appelö. Extended abstract, Waves 2015.
Hermite methods for hyperbolic-parabolic systems
T. Hagstrom, D. Appelö and C. Y. Jang. In Waves 2011, Vancouver, Canada, 2011.
A stable finite difference method for the elastic wave equation on complex domains with free surface boundary conditions
D. Appelö, S. Nilsson, A. N. Petersson and B. Sjögreen. In Proceedings of Waves 2007, Reading, UK, 2007.
A new PML for the simulation of elastic waves in anisotropic media
D. Appelö and G. Kreiss. In The 7th Int. Conf. on Math. and Num. Aspects of Wave Propagation, Brown University, 2005.
Discretely nonreflecting boundary conditions for higher order centered schemes for wave equations
D. Appelö and G. Kreiss. In Cohen et al., editor, Mathematical and Numerical Aspects of Wave Propagation, Proceedings Waves 2003, pages 125-130. Springer Verlag, 2003.
Theses
Absorbing layers and non-reflecting boundary conditions for wave propagation problems
D. Appelö. PhD thesis, Royal Institute of Technology, October 2005.
Non-reflecting boundary conditions for wave propagation problems
D. Appelö. Licenciate thesis, Royal Institute of Technology, 2003.
PML-methods for the linearized Euler equations
D. Appelö. Master's thesis, Royal Institute of Technology, 2000.