Alexander Ostermann

CoRR, February, 2025

2024

Accelerating Exponential Integrators to Efficiently Solve Semilinear Advection-Diffusion-Reaction Equations.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2024

Low Regularity Full Error Estimates for the Cubic Nonlinear Schrödinger Equation.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2024

Highly efficient NURBS-based isogeometric analysis for coupled nonlinear diffusion-reaction equations with and without advection.

[BibT_eX]

[DOI]

Ilham Asmouh

J. Comput. Sci., 2024

Should exponential integrators be used for advection-dominated problems?

[BibT_eX]

[DOI]

Trung Hau Hoang

CoRR, 2024

The exponential trapezoidal method for semilinear integro-differential equations.

[BibT_eX]

[DOI]

Nasrin Vaisi

CoRR, 2024

Filtered Lie-Trotter splitting for the "good" Boussinesq equation: low regularity error estimates.

[BibT_eX]

[DOI]

CoRR, 2024

2023

A robust and conservative dynamical low-rank algorithm.

[BibT_eX]

[DOI]

Carmela Scalone

J. Comput. Phys., July, 2023

Explicit Exponential Runge-Kutta Methods for Semilinear Integro-Differential Equations.

[BibT_eX]

[DOI]

Fardin Saedpanah

Nasrin Vaisi

SIAM J. Numer. Anal., June, 2023

Low regularity error estimates for high dimensional nonlinear Schrödinger equations.

[BibT_eX]

[DOI]

Lun Ji

CoRR, 2023

Accelerating exponential integrators to efficiently solve advection-diffusion-reaction equations.

[BibT_eX]

[DOI]

CoRR, 2023

Low regularity error estimates for the time integration of 2D NLS.

[BibT_eX]

[DOI]

CoRR, 2023

2022

A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions.

[BibT_eX]

[DOI]

Mirko Residori

Numerische Mathematik, 2022

Error estimates at low regularity of splitting schemes for NLS.

[BibT_eX]

[DOI]

Frédéric Rousset

Math. Comput., 2022

Exponential Integrators for Second-Order in Time Partial Differential Equations.

[BibT_eX]

[DOI]

Duy Phan

J. Sci. Comput., 2022

A Fully Discrete Low-Regularity Integrator for the Nonlinear Schrödinger Equation.

[BibT_eX]

[DOI]

Fangyan Yao

J. Sci. Comput., 2022

A μ-mode integrator for solving evolution equations in Kronecker form.

[BibT_eX]

[DOI]

J. Comput. Phys., 2022

2021

A Preconditioning Technique for an All-at-once System from Volterra Subdiffusion Equations with Graded Time Steps.

[BibT_eX]

[DOI]

Yong-Liang Zhao

Xian-Ming Gu

J. Sci. Comput., 2021

Fast IIF-WENO Method on Non-uniform Meshes for Nonlinear Space-Fractional Convection-Diffusion-Reaction Equations.

[BibT_eX]

[DOI]

J. Sci. Comput., 2021

A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations.

[BibT_eX]

[DOI]

Yong-Liang Zhao

Xian-Ming Gu

J. Comput. Phys., 2021

An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs.

[BibT_eX]

[DOI]

J. Comput. Phys., 2021

A pseudo-spectral splitting method for linear dispersive problems with transparent boundary conditions.

[BibT_eX]

[DOI]

Mirko Residori

J. Comput. Appl. Math., 2021

Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity.

[BibT_eX]

[DOI]

Frédéric Rousset

Found. Comput. Math., 2021

An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware.

[BibT_eX]

[DOI]

Mirko Residori

Comput. Phys. Commun., 2021

A second order low-regularity integrator for the nonlinear Schrödinger equation.

[BibT_eX]

[DOI]

Fangyan Yao

Yifei Wu

CoRR, 2021

A μ-mode integrator for solving evolution equations in Kronecker form.

[BibT_eX]

[DOI]

CoRR, 2021

Fast numerical schemes for nonlinear space-fractional multidelay reaction-diffusion equations by implicit integration factor methods.

[BibT_eX]

[DOI]

Appl. Math. Comput., 2021

2020

On the convergence of Lawson methods for semilinear stiff problems.

[BibT_eX]

[DOI]

Jan Leibold

Numerische Mathematik, 2020

A low-rank projector-splitting integrator for the Vlasov-Maxwell equations with divergence correction.

[BibT_eX]

[DOI]

J. Comput. Phys., 2020

An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation.

[BibT_eX]

[DOI]

CoRR, 2020

A parallel preconditioning technique for an all-at-once system from subdiffusion equations with variable time steps.

[BibT_eX]

[DOI]

Yong-Liang Zhao

Xian-Ming Gu

CoRR, 2020

Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces.

[BibT_eX]

[DOI]

Frédéric Rousset

CoRR, 2020

2019

Convergence of a Low-Rank Lie-Trotter Splitting for Stiff Matrix Differential Equations.

[BibT_eX]

[DOI]

Hanna Walach

SIAM J. Numer. Anal., 2019

A Fourier Integrator for the Cubic Nonlinear Schrödinger Equation with Rough Initial Data.

[BibT_eX]

[DOI]

Marvin Knöller

SIAM J. Numer. Anal., 2019

Two exponential-type integrators for the "good" Boussinesq equation.

[BibT_eX]

[DOI]

Chunmei Su

Numerische Mathematik, 2019

2018

Analysis for Computer Scientists - Foundations, Methods, and Algorithms, Second Edition

[BibT_eX]

[DOI]

Michael Oberguggenberger

Undergraduate Topics in Computer Science, Springer, ISBN: 978-3-319-91154-0, 2018

Numerical low-rank approximation of matrix differential equations.

[BibT_eX]

[DOI]

Hermann Mena

Lena-Maria Pfurtscheller

J. Comput. Appl. Math., 2018

Low Regularity Exponential-Type Integrators for Semilinear Schrödinger Equations.

[BibT_eX]

[DOI]

Found. Comput. Math., 2018

Magnus integrators on multicore CPUs and GPUs.

[BibT_eX]

[DOI]

Comput. Phys. Commun., 2018

A split step Fourier/discontinuous Galerkin scheme for the Kadomtsev-Petviashvili equation.

[BibT_eX]

[DOI]

Appl. Math. Comput., 2018

Efficient boundary corrected Strang splitting.

[BibT_eX]

[DOI]

Martina Moccaldi

Appl. Math. Comput., 2018

2017

A splitting approach for the magnetic Schrödinger equation.

[BibT_eX]

[DOI]

Marco Caliari

J. Comput. Appl. Math., 2017

Splitting methods for constrained diffusion-reaction systems.

[BibT_eX]

[DOI]

Robert Altmann

Comput. Math. Appl., 2017

2016

Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 2: Oblique Boundary Conditions.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2016

The Leja Method Revisited: Backward Error Analysis for the Matrix Exponential.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2016

Evaluation of the partitioned global address space (PGAS) model for an inviscid Euler solver.

[BibT_eX]

[DOI]

Martina Prugger

Parallel Comput., 2016

The error structure of the Douglas-Rachford splitting method for stiff linear problems.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2016

Parallel exponential Rosenbrock methods.

[BibT_eX]

[DOI]

Comput. Math. Appl., 2016

2015

Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 1: Dirichlet Boundary Conditions.

[BibT_eX]

[DOI]

SIAM J. Sci. Comput., 2015

A splitting approach for the Kadomtsev-Petviashvili equation.

[BibT_eX]

[DOI]

J. Comput. Phys., 2015

Fast algorithms for morphological operations using run-length encoded binary images.

[BibT_eX]

[DOI]

Gregor Ehrensperger

Felix Schwitzer

CoRR, 2015

On the error propagation of semi-Lagrange and Fourier methods for advection problems.

[BibT_eX]

[DOI]

Comput. Math. Appl., 2015

2014

Convergence Analysis of a Discontinuous Galerkin/Strang Splitting Approximation for the Vlasov-Poisson Equations.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2014

Convergence Analysis of Strang Splitting for Vlasov-Type Equations.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2014

A Moment-Matching Arnoldi Iteration for Linear Combinations of φ Functions.

[BibT_eX]

[DOI]

Antti Koskela

SIAM J. Matrix Anal. Appl., 2014

Reprint of "Explicit exponential Runge-Kutta methods of high order for parabolic problems".

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2014

Exponential Rosenbrock methods of order five - construction, analysis and numerical comparisons.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2014

Explicit exponential Runge-Kutta methods of high order for parabolic problems.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2014

An almost symmetric Strang splitting scheme for the construction of high order composition methods.

[BibT_eX]

[DOI]

J. Comput. Appl. Math., 2014

An almost symmetric Strang splitting scheme for nonlinear evolution equations.

[BibT_eX]

[DOI]

Comput. Math. Appl., 2014

2013

Meshfree Exponential Integrators.

[BibT_eX]

[DOI]

Marco Caliari

Stefan Rainer

SIAM J. Sci. Comput., 2013

Stability of Exponential Operator Splitting Methods for Noncontractive Semigroups.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2013

Exponential B-Series: The Stiff Case.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2013

Exponential Taylor methods: Analysis and implementation.

[BibT_eX]

[DOI]

Antti Koskela

Comput. Math. Appl., 2013

Exponential integrators on graphic processing units.

[BibT_eX]

[DOI]

Proceedings of the International Conference on High Performance Computing & Simulation, 2013

2012

Stiff Order Conditions for Exponential Runge-Kutta Methods of Order Five.

[BibT_eX]

[DOI]

Proceedings of the Modeling, Simulation and Optimization of Complex Processes, 2012

2011

Analysis for Computer Scientists - Foundations, Methods, and Algorithms.

[BibT_eX]

[DOI]

Michael Oberguggenberger

Undergraduate Topics in Computer Science, Springer, ISBN: 978-0-85729-446-3, 2011

2010

Exponential integrators.

[BibT_eX]

[DOI]

Acta Numer., 2010

2009

Exponential splitting for unbounded operators.

[BibT_eX]

[DOI]

Math. Comput., 2009

A minimisation approach for computing the ground state of Gross-Pitaevskii systems.

[BibT_eX]

[DOI]

J. Comput. Phys., 2009

2008

Exponential Rosenbrock-Type Methods.

[BibT_eX]

[DOI]

Julia Schweitzer

SIAM J. Numer. Anal., 2008

Finite Element Runge-Kutta Discretizations of Porous Medium-Type Equations.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2008

Dimension splitting for evolution equations.

[BibT_eX]

[DOI]

Numerische Mathematik, 2008

2005

Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems.

[BibT_eX]

[DOI]

SIAM J. Numer. Anal., 2005

2002

Backward Euler discretization of fully nonlinear parabolic problems.

[BibT_eX]

[DOI]

Math. Comput., 2002

Long-term stability of variable stepsize approximations of semigroups.

[BibT_eX]

[DOI]

Nikolai Bakaev

Math. Comput., 2002

2000

Shadowing for Nonautonomous Parabolic Problems with Applications to Long-Time Error Bounds.

[BibT_eX]

[DOI]

Cesar Palencia

SIAM J. Numer. Anal., 2000

1998

Hopf bifurcation of reaction-diffusion and Navier-Stokes equations under discretization.

[BibT_eX]

[DOI]

Christian Lubich

Numerische Mathematik, 1998

1990

Continuous extensions of Rosenbrock-type methods.

[BibT_eX]

[DOI]

Computing, 1990

1986

The solution of a combustion problem with Rosenbrock methods.

[BibT_eX]

[DOI]

Peter Kaps

Tien Dai Bui

ACM Trans. Math. Softw., 1986

1977

Hermitesche Differenzenverfahren zur Approximation der Lösung von Differentialgleichungen der Formuxy=f(x, y, u, ux, uy).

[BibT_eX]

[DOI]