An Efficient HPC Framework for Parallel Long-Time and Large-Scale Simulation of a Class of Anomalous Single-Phase Models

Alyoubi, Ahmad; Ganesh, M.

doi:10.1109/hpcc-css-icess.2015.197

Cited by 1 publication

(3 citation statements)

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“…In this section, we demonstrate the algorithm described in previous sections, in conjunction with parallel implementation following our hybrid computational framework in [16]. We demonstrate that such an efficient framework facilitates obtaining excellent parallel performance and be able to solve mixed-FEM models with large degrees of freedom.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Hence, it is a non-trivial task to carry out the parallel-in-time-and-space implementation of the above approach, after discretizing in the spatial variable using the standard Galerkin FEM or FDM approach with large DoF. Such a framework was developed by the authors in [16] for the second-order PDE based formulation.…”

Section: Second-order Pde Based Lt-ilt Formulationmentioning

confidence: 99%

“…For our implementation, we use a hybrid parallel-in-time and parallel-in-space approach by developing several MPI communicators and memory efficient organization of setting up algebraic system that facilitate subdivision of parallel tasks in time and space. For details of our hybrid HPC framework, we refer the reader to [16] and related references therein.…”

Section: Numerical Experimentsmentioning

confidence: 99%

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Parallel mixed FEM simulation of a class of single-phase models with non-local operators

Alyoubi

Ganesh

2016

Journal of Computational and Applied Mathematics

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Anomalous sub-diffusion processes governed by non-local operators have been used in various applications. These are recently adapted to model complex single-and multi-phase fluid flow in unconventional reservoirs to understand the long-time behavior of various quantities of interest. Such processes, requiring long-time simulation, are modeled by a non-local in-time fractional derivative based Darcy's law and a conservation of mass equation, leading to a coupled system of first-order fractional partial differential equations (FPDEs). Standard time-stepping discretization of these continuous models lead to computational bottleneck for long-time simulation. Memory limitations [in each node of high performance computing (HPC) clusters] dictate computational constraints for resolving fine scale spatial structures in the models. We describe and implement a parallel-in-time and parallel-in-space mixed finite element (FEM) based discretization computer model to simulate the FPDEs. Our hybrid parallel-in-time-and-space framework facilitates efficient long-time simulation of the first-order computer model to overcome the time-stepping computational bottleneck and, within the node memory constraints, approximate the continuous models with large degrees of freedom (DoF).

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Second-order Pde Based Lt-ilt Formulationmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

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