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EngwerEtAl2025
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<span id="EngwerEtAl2025">C. Engwer, A. Schell, and N.-A. Dreier, “Vectorised Parallel in Time methods for low-order discretizations with application to Porous Media problems,” arXiv:2504.02117v1 [math.NA], 2025 [Online]. Available at: <a href="http://arxiv.org/abs/2504.02117v1" target="_blank">http://arxiv.org/abs/2504.02117v1</a></span>
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BibTeX entry <code>EngwerEtAl2025</code>
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<pre class="abstract">@unpublished{EngwerEtAl2025,
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author = {Engwer, Christian and Schell, Alexander and Dreier, Nils-Arne},
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howpublished = {arXiv:2504.02117v1 [math.NA]},
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title = {Vectorised Parallel in Time methods for low-order discretizations with application to Porous Media problems},
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url = {http://arxiv.org/abs/2504.02117v1},
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year = {2025}
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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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