In: Computers and mathematics with applications, 2021, vol. 99, p. 162-170
We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multigrid strategies. For both approaches, we start from an integral formulation of the continuous time dependent problem. Then, a collocation form for PFASST and a discontinuous ...
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In: Journal of computational physics, 2021, vol. 433, p. 17 p
We present a novel approach aimed at high-performance uncertainty quantification for time-dependent problems governed by partial differential equations. In particular, we consider input uncertainties described by a Karhunen-Loève expansion and compute statistics of high-dimensional quantities-of-interest, such as the cardiac activation potential. Our methodology relies on a close integration...
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Thèse de doctorat : Università della Svizzera italiana, 2020 ; 2020INFO005.
The goal of this thesis is to design and study an efficient strategy to solve possibly non-linear parabolic partial differential equations on massively parallel machines. Traditionally, when solving time-dependent problems, time stepping methods are used to advance the solution in time. These techniques are inherently sequential and therefore they introduce a bottleneck in the overall...
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