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Publications

Submitted Journal articles

  1. (with Ferrari, M.) Generalized convolution quadrature based on the trapezoidal rule. Submitted 2023 arXiv:2305.11134

  2. (with Ferrari, M.) Runge-Kutta convolution quadrature based on Gauss methods. Submitted 2022 arXiv:2212.07170

  3. (with Baker, K. and Ptashnyk, M.) Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping. Submitted 2022 arXiv:2210.16349

Book

  1. (with Sayas, F.J.) Integral Equation Methods for Evolutionary PDE: A Convolution Quadrature Approach, Springer Series in Computational Mathematics (SSCM, volume 59), 2022

Published/Accepted Journal articles

  1. (with Trefethen L. N.) Numerical solution of the omitted area problem of univalent function theory. Comput. Methods Funct. Theory 1(1), 259-267, 2001.

  2. (with Trefethen, L. N.) A multipole method for Schwarz-Christoffel mapping of polygons with thousands of sides. SIAM J. Sci. Comp. 25(3), 1042-1065, 2003.

  3. Eigenfrequencies of fractal drums. J. Comput. Appl. Math. 198(1), 1-18, 2007.

  4. (with Hackbusch W.) Hierarchical matrix techniques for low and high frequency Helmholtz problems, IMA J. Numer. Anal.,28, 46–79, 2008.

  5. (with Sauter, S.) A refined Galerkin error and stability analysis for highly indefinite variational problems, SIAM J. on Num. Anal., 45(1), 37–53, 2007.

  6. Revisiting the crowding phenomenon in Schwarz-Christoffel conformal mapping, SIAM J. Sci. Comput. 30(2), 618–636, 2008.

  7. (with Sauter, S.) Rapid solution of the wave equation in unbounded domains, SIAM J. Numer. Anal. 47, 227–249, 2008.

  8. (with Boerm, S., and Sauter, S.) FEM for Elliptic Eigenvalue Problems: How Coarse Can the Coarsest Mesh be Chosen? An Experimental Study., Comp. and Visualisation in Science, 11, no. 4-6, 363–372, 2008.

  9. Multistep and multistage convolution quadrature for the wave equation: Algorithms and experiments, SIAM J. Sci. Comput., 32(5), 2964–2994, 2010.

  10. (with Lubich Ch.) An error analysis of Runge-Kutta convolution quadrature, BIT, 51(3), 483–496, 2011.

  11. (with Schanz M.) Wave Propagation Problems treated with Convolution Quadrature and BEM, invited chapter in the book “Fast Boundary Element Methods in Engineering and Industrial Applications”, edited by U. Langer, M. Schanz, O. Steinbach, and W. L. Wendland, 2012.

  12. (with Melenk J.M., and Lubich Ch.) Runge-Kutta convolution quadrature for operators arising in wave propagation, Numer. Math., 119(1), 1–20, 2011.

  13. (with Gruhne V.) Efficient long time computations of time-domain boundary integrals for 2D and dissipative wave equations, J. Comput. Appl. Math., 235(14), 4207–4220, 2011.

  14. (with Peterseim, D.) Parallel multistep methods for linear evolution problems, IMA J. Numer. Anal., 32, 1217–1240, 2012.

  15. (with Messner, M., and Schanz, M.) Runge-Kutta convolution quadrature for the Boundary Element Method, Computer Methods in Applied Mechanics and Engineering, Volumes 245–246, pg. 90-101, 2012.

  16. (with Ballani, J., Sauter, S., and Veit, A.) Numerical Solution of Exterior Maxwell Problems by Galerkin BEM and Runge-Kutta Convolution Quadrature, Numer. Math., 123(4), 643–670, 2013.

  17. Time-domain Dirichlet-to-Neumann map and its discretization, IMA J. Numer. Anal. 34, no. 3, 1136-1155, 2014 IMA J. Numer. Anal., 2013.

  18. (with Kachanovska, M.) Sparsity of Runge-Kutta convolution weights for the three-dimensional wave equation, BIT 54, no. 4, 901-936, 2014. MPI Preprint

  19. (with Kachanovska, M.) Fast convolution quadrature for the wave equation in three dimensions, J. Comput. Phys. 276, 103-126, 2014. MPI Preprint

  20. (with Laliena, A., and Sayas, F.J.) Fully discrete versions of Kirchhoff ’s formula with CQ-BEM, IMA J. Numer. Anal. 35, 859-884, 2014. arXiv:1301.0267

  21. (with Lubich, Ch., and Sayas, F.J.) Stable numerical coupling of exterior and interior problems for the wave equation, Numer. Math. 129, no. 4, 611-646, 2015. arXiv:1309.2649

  22. (with Georgoulis, E.H. and Lijoka, O.) A Trefftz polynomial space-time discontinuous Galerkin method for the second order wave equation, SIAM J. Numer. Anal., 55(1), 2016, arXiv:1610.01878.

  23. (with López-Fernández, M and Schädle, A.) Fast and oblivious algorithms for dissipative and 2D wave equations, SIAM J. Numer. Anal., 55(2), 2017, arXiv:1604.04135.

  24. (with Rieder, A.) Convolution quadrature for the wave equation with a nonlinear impedance boundary condition, Math. Comp., 87, no. 312, 2018, arXiv:1604.05212.

  25. (with Lubich, C.) Runge-Kutta convolution coercivity and its use for time-dependent boundary integral equations, IMA J. Numer. Anal., 39(3), 2019, arXiv:1702.08385

  26. (with Melenk, J.M., Nochetto, R.H., Otárola, E., Salgado, A.J., Schwab, C.) Tensor FEM for spectral fractional diffusion, Foundations of Computational Mathematics volume 19, 901–962(2019), arXiv:1707.07367

  27. (with López-Fernández, M.) Efficient high order algorithms for fractional integrals and associated fractional differential equations, Numer. Math., 141(2), 2019, arxiv:1803.00642

  28. (with Otárola, E.) A PDE approach to fractional diffusion: a space-fractional wave equation, Numer. Math., 143(1), 2019 arxiv:1806.06030

  29. (with Boulton, L.) Computation of sharp estimates of the Poincaré constant on planar domains with piecewise self-similar boundary, accepted for publication in Journal of Fractal Geometry, 2019, arxiv:1708.08401

  30. (with López-Fernández, M.) Numerical approximation of the Schrödinger equation with concentrated potential, accepted for publication in Journal of Computational Physics 2019, arxiv:1908:01292

  31. (with, Lubich, C, Nick, J.) Time-dependent acoustic scattering from generalized impedance boundary conditions via boundary elements and convolution quadrature IMA JNA, 2020, arXiv:2005:13880

  32. (with Baker, K.) Numerical analysis of a wave equation for lossy media obeying a frequency power law, accepted for publication in IMA JNA 2021, arXiv:2012.04520

  33. (with, Lord, G., Molla, J.) Strong convergence of a Verlet integrator for the semi-linear stochastic wave equation, accepted for publication in SINUM, 2021, arXiv:2009.07710

  34. (with Makridakis, C.G.) A posteriori error analysis for approximations of time-fractional subdiffusion problems, accepted for publication in Math. Comp., 2022 arXiv:2203.00340

  35. Implicit/explicit, BEM/FEM coupled scheme for acoustic waves with the wave equation in the second order formulation, accepted for publication in CMAM (Special issue dedicated to F-J Sayas) 2022 arXiv:2203.00986

  36. (with Aldahham, E.) A modified convolution quadrature combined with the method of fundamental solutions and Galerkin BEM for acoustic scattering, accepted for publication in Communications in Computational Physics 2022, arXiv:2203.00996

  37. (with, Melenk, J.M., Schwab, C.) hp-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains, accepted for publication in IMA JNA, 2022, arXiv:2004.10517

  38. (with, Melenk, J.M,. Schwab, C.) Exponential Convergence of hp FEM for Spectral Fractional Diffusion in Polygons, accepted for publication in Numerische Mathematik, 2022, arXiv:2011.05701

Selected Proceedings

  1. (with Zhang Y.) A family of efficient numerical solvers of time domain boundary integral equations, Forum Acusticum 2011, Aalborg. final version

Theses

  1. Computation of Conformal Maps by Fast Multipole Method Accelerated Schwarz-Christoffel Transformation, D.Phil., University of Oxford, 2003.

  2. Time-domain boundary integral equations for wave propagation and their numerical solution, Habilitation, University of Dusseldorf, 2012