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abstract = {We investigate parallel performance of parallel spectral deferred corrections, a numerical approach that provides small-scale parallelism for the numerical solution of initial value problems. The scheme is applied to the shallow water equation and uses an IMEX splitting that integrates fast modes implicitly and slow modes explicitly in order to be efficient. We describe parallel $\texttt{OpenMP}$-based implementations of parallel SDC in two well established simulation codes: the finite volume based operational ocean model $\texttt{ICON-O}$ and the spherical harmonics based research code $\texttt{SWEET}$. The implementations are benchmarked on a single node of the JUSUF ($\texttt{SWEET}$) and JUWELS ($\texttt{ICON-O}$) system at J\"ulich Supercomputing Centre. We demonstrate a reduction of time-to-solution across a range of accuracies. For $\texttt{ICON-O}$, we show speedup over the currently used Adams--Bashforth-2 integrator with $\texttt{OpenMP}$ loop parallelization. For $\texttt{SWEET}$, we show speedup over serial spectral deferred corrections and a second order implicit-explicit integrator.},
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author = {Philip Freese and Sebastian Götschel and Thibaut Lunet and Daniel Ruprecht and Martin Schreiber},
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year = {2025},
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}
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@inbook{EndtmayerEtAl2025,
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author = {Endtmayer, Bernhard and Schafelner, Andreas},
abstract = {High order methods have shown great potential to overcome performance issues of simulations of partial differential equations (PDEs) on modern hardware, still many users stick to low-order, matrixbased simulations, in particular in porous media applications. Heterogeneous coefficients and low regularity of the solution are reasons not to employ high order discretizations. We present a new approach for the simulation of instationary PDEs that allows to partially mitigate the performance problems. By reformulating the original problem we derive a parallel in time time integrator that increases the arithmetic intensity and introduces additional structure into the problem. By this it helps accelerate matrix-based simulations on modern hardware architectures. Based on a system for multiple time steps we will formulate a matrix equation that can be solved using vectorised solvers like Block Krylov methods. The structure of this approach makes it applicable for a wide range of linear and nonlinear problems. In our numerical experiments we present some first results for three different PDEs, a linear convection-diffusion equation, a nonlinear diffusion-reaction equation and a realistic example based on the Richards' equation.},
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author = {Christian Engwer and Alexander Schell and Nils-Arne Dreier},
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