Publications
Submitted Journal articles
(with Ferrari, M.) Generalized convolution quadrature based on the
trapezoidal rule. Submitted 2023 arXiv:2305.11134
Book
(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
(with Trefethen L. N.) Numerical solution of the omitted area
problem of univalent function theory. Comput. Methods Funct. Theory 1(1),
259-267, 2001.
(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.
Eigenfrequencies of fractal drums. J. Comput. Appl. Math.
198(1), 1-18, 2007.
(with Hackbusch W.) Hierarchical matrix techniques for low and
high frequency Helmholtz problems, IMA J. Numer. Anal.,28, 46–79, 2008.
(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.
Revisiting the crowding phenomenon in Schwarz-Christoffel
conformal mapping, SIAM J. Sci. Comput. 30(2), 618–636, 2008.
(with Sauter, S.) Rapid solution of the wave equation in
unbounded domains, SIAM J. Numer. Anal. 47, 227–249, 2008.
(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.
Multistep and multistage convolution quadrature for the wave
equation: Algorithms and experiments, SIAM J. Sci. Comput., 32(5),
2964–2994, 2010.
(with Lubich Ch.) An error analysis of Runge-Kutta
convolution
quadrature, BIT, 51(3), 483–496, 2011.
(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.
(with Melenk J.M., and Lubich Ch.) Runge-Kutta convolution
quadrature for operators arising in wave propagation, Numer. Math.,
119(1), 1–20, 2011.
(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.
(with Peterseim, D.) Parallel multistep methods for
linear
evolution problems, IMA J. Numer. Anal., 32, 1217–1240, 2012.
(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.
(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.
Time-domain Dirichlet-to-Neumann map and its
discretization, IMA J. Numer. Anal. 34, no. 3, 1136-1155, 2014
IMA J. Numer. Anal.,
2013.
(with Kachanovska, M.) Sparsity of Runge-Kutta convolution
weights for the three-dimensional wave equation, BIT 54, no. 4, 901-936,
2014. MPI Preprint
(with Kachanovska, M.) Fast convolution quadrature for the
wave equation in three dimensions, J. Comput. Phys. 276, 103-126,
2014. MPI Preprint
(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
(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
(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.
(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.
(with Rieder, A.) Convolution quadrature for the wave equation with a
nonlinear impedance boundary condition, Math. Comp., 87, no. 312, 2018,
arXiv:1604.05212.
(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
(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
(with López-Fernández, M.) Efficient high order algorithms for
fractional integrals and associated fractional differential equations,
Numer. Math., 141(2), 2019, arxiv:1803.00642
(with Otárola, E.) A PDE approach to fractional diffusion: a
space-fractional wave equation, Numer. Math., 143(1), 2019 arxiv:1806.06030
(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
(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
(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
(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
(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
(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
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
(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
(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
(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
(with Baker, K. and Ptashnyk, M.)
Numerical analysis of a time-stepping method for the Westervelt equation
with time-fractional damping.
Published in Mathematics of Computation, 2024 arXiv:2210.16349
(with Ferrari, M.) Runge-Kutta convolution quadrature based on Gauss
methods. Accepted for publication in Numerische Mathematik 2024
arXiv:2212.07170
Selected Proceedings
(with Zhang Y.) A family of efficient numerical solvers of time
domain boundary integral equations, Forum Acusticum 2011, Aalborg. final version
Theses
Computation of Conformal Maps by Fast Multipole Method Accelerated
Schwarz-Christoffel Transformation, D.Phil., University of Oxford, 2003.
Time-domain boundary integral equations for
wave propagation and their numerical solution, Habilitation, University of
Dusseldorf, 2012
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