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Journal of Scientific Computing

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24-11-2017

HiMod Reduction of Advection–Diffusion–Reaction Problems with General Boundary Conditions

Authors: Matteo C. Aletti, Simona Perotto, Alessandro Veneziani

Published in: Journal of Scientific Computing | Issue 1/2018

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Abstract

We extend the hierarchical model reduction procedure previously introduced in Ern et al. (in: Kunisch, Of, Steinbach (eds) Numerical mathematics and advanced applications, Springer, Berlin, pp 703–710, 2008) and Perotto et al. (Multiscale Model Simul 8(4):1102–1127, 2010) to deal with general boundary conditions, enforcing their prescription in the basis function set. This is achieved by solving a Sturm–Liouville Eigenvalue problem. We analyze this approach and provide a convergence analysis for the associated error in the case of a linear advection–diffusion–reaction problem in rectangles (2D) and slabs (3D). Numerical results confirm the theoretical investigation and the reliability of the proposed approach.

previous article Global Convergence of Unmodified 3-Block ADMM for a Class of Convex Minimization Problems

next article An Efficient Lagrangian Interpolation Scheme for Computing Flow Maps and Line Integrals using Discrete Velocity Data

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Title: HiMod Reduction of Advection–Diffusion–Reaction Problems with General Boundary Conditions
Authors: Matteo C. Aletti
Simona Perotto
Alessandro Veneziani
Publication date: 24-11-2017
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0614-5

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