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08/09/2023
Functional-preserving predictor-corrector multiderivative schemes
In this work, we develop a class of high-order multiderivative time inte...
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07/24/2023
Stability of step size control based on a posteriori error estimates
A posteriori error estimates based on residuals can be used for reliable...
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04/05/2023
Modeling still matters: a surprising instance of catastrophic floating point errors in mathematical biology and numerical methods for ODEs
We guide the reader on a journey through mathematical modeling and numer...
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02/27/2023
Resolving Entropy Growth from Iterative Methods
We consider entropy conservative and dissipative discretizations of nonl...
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02/24/2023
A discontinuous Galerkin discretization of elliptic problems with improved convergence properties using summation by parts operators
Nishikawa (2007) proposed to reformulate the classical Poisson equation ...
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11/04/2022
Bridging HPC Communities through the Julia Programming Language
The Julia programming language has evolved into a modern alternative to ...
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09/15/2022
On error-based step size control for discontinuous Galerkin methods for compressible fluid dynamics
We study temporal step size control of explicit Runge-Kutta methods for ...
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03/19/2022
On the entropy projection and the robustness of high order entropy stable discontinuous Galerkin schemes for under-resolved flows
High order entropy stable schemes provide improved robustness for comput...
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01/11/2022
A Note on Numerical Fluxes Conserving Harten's Entropies for the Compressible Euler Equations
Entropy-conserving numerical fluxes are a cornerstone of modern high-ord...
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12/20/2021
Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws
Many modern discontinuous Galerkin (DG) methods for conservation laws ma...
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11/23/2021
Computing with B-series
We present BSeries.jl, a Julia package for the computation and manipulat...
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08/16/2021
A New Stability Approach for Positivity-Preserving Patankar-type Schemes
Patankar-type schemes are linearly implicit time integration methods des...
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08/14/2021
Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing
We present Trixi.jl, a Julia package for adaptive high-order numerical s...
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04/14/2021
Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics
We develop error-control based time integration algorithms for compressi...
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02/15/2021
On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations
We study the numerical error in solitary wave solutions of nonlinear dis...
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09/28/2020
Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes
Recently, it was discovered that the entropy-conserving/dissipative high...
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09/21/2020
A conservative fully-discrete numerical method for the regularised shallow water wave equations
The paper proposes a new, conservative fully-discrete scheme for the num...
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08/24/2020
A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics
One of the challenges when simulating astrophysical flows with self-grav...
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07/17/2020
Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts
We study nonlinear hyperbolic conservation laws with non-convex flux and...
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06/26/2020
A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
We develop general tools to construct fully-discrete, conservative numer...
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05/13/2020
Positivity-Preserving Adaptive Runge-Kutta Methods
Many important differential equations model quantities whose value must ...
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03/19/2020
Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
Recently, relaxation methods have been developed to guarantee the preser...
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03/09/2020
A Class of A Stable Summation by Parts Time Integration Schemes
Since integration by parts is an important tool when deriving energy or ...
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03/08/2020
Towards Green Computing: A Survey of Performance and Energy Efficiency of Different Platforms using OpenCL
When considering different hardware platforms, not just the time-to-solu...
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03/06/2020
General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes
Recently, an approach known as relaxation has been developed for preserv...
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01/14/2020
Relaxation Runge-Kutta Methods for Hamiltonian Problems
The recently-introduced relaxation approach for Runge-Kutta methods can ...
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11/21/2019
On the robustness and performance of entropy stable discontinuous collocation methods for the compressible Navier-Stokes equations
In computational fluid dynamics, the demand for increasingly multidiscip...
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11/21/2019
On the robustness and performance of entropy stable discontinuous collocation methods for the compressible Navie-Stokes equations
In computational fluid dynamics, the demand for increasingly multidiscip...
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09/29/2019
Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems
Many important initial value problems have the property that energy is n...
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08/23/2019
Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators
In this article, discrete variants of several results from vector calcul...
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08/13/2019