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03/28/2023
Accelerating exponential integrators to efficiently solve advection-diffusion-reaction equations
In this paper we consider an approach to improve the performance of expo...
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01/25/2023
Low regularity error estimates for the time integration of 2D NLS
A filtered Lie splitting scheme is proposed for the time integration of ...
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06/19/2022
A robust and conservative dynamical low-rank algorithm
Dynamical low-rank approximation, as has been demonstrated recently, can...
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06/12/2022
Explicit exponential Runge-Kutta methods for semilinear integro-differential equations
The aim of this paper is to construct and analyze explicit exponential R...
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11/29/2021
Exponential integrators for second-order in time partial differential equations
Two types of second-order in time partial differential equations (PDEs),...
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09/02/2021
A second order low-regularity integrator for the nonlinear Schrödinger equation
In this paper, we analyse a new exponential-type integrator for the nonl...
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08/10/2021
A fully discrete low-regularity integrator for the nonlinear Schrödinger equation
For the solution of the cubic nonlinear Schrödinger equation in one spac...
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03/10/2021
An exponential integrator/WENO discretization for sonic-boom simulation on modern computer hardware
Recently a splitting approach has been presented for the simulation of s...
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03/02/2021
A μ-mode integrator for solving evolution equations in Kronecker form
In this paper, we propose a μ-mode integrator for computing the solution...
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12/28/2020
Error estimates at low regularity of splitting schemes for NLS
We study a filtered Lie splitting scheme for the cubic nonlinear Schrödi...
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11/04/2020
An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation
The space fractional Cahn-Hilliard phase-field model is more adequate an...
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10/11/2020
A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations
Fractional Ginzburg-Landau equations as the generalization of the classi...
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08/26/2020
An accurate and time-parallel rational exponential integrator for hyperbolic and oscillatory PDEs
Rational exponential integrators (REXI) are a class of numerical methods...
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07/29/2020
A parallel preconditioning technique for an all-at-once system from subdiffusion equations with variable time steps
Volterra subdiffusion problems with weakly singular kernel describe the ...
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06/23/2020
Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces
In this paper, we propose a new scheme for the integration of the period...
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06/09/2020
A pseudo-spectral Strang splitting method for linear dispersive problems with transparent boundary conditions
The present work proposes a second-order time splitting scheme for a lin...
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01/14/2016
Evaluation of the Partitioned Global Address Space (PGAS) model for an inviscid Euler solver
In this paper we evaluate the performance of Unified Parallel C (which i...
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04/04/2015