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9 changes: 9 additions & 0 deletions _bibliography/pint.bib
Original file line number Diff line number Diff line change
Expand Up @@ -7572,6 +7572,15 @@ @unpublished{EggerEtAl2025
year = {2025},
}

@unpublished{EngwerEtAl2025,
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.},
author = {Christian Engwer and Alexander Schell and Nils-Arne Dreier},
howpublished = {arXiv:2504.02117v1 [math.NA]},
title = {Vectorised Parallel in Time methods for low-order discretizations with application to Porous Media problems},
url = {http://arxiv.org/abs/2504.02117v1},
year = {2025},
}

@article{FungEtAl2025,
author = {Fung, Po Yin and Hon, Sean Y.},
doi = {10.1016/j.camwa.2025.01.019},
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