GATIPOR SIGNED
Guaranteed fully adaptive algorithms with tailored inexact solvers for complex porous media flows
Total Cost €
0EC-Contrib. €
0Partnership
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Explore the words cloud of the GATIPOR project. It provides you a very rough idea of what is the project "GATIPOR" about.
Project "GATIPOR" data sheet
The following table provides information about the project.
| Coordinator |
INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE
Organization address contact info |
| Coordinator Country | France [FR] |
| Project website | https://project.inria.fr/gatipor/ |
| Total cost | 1˙283˙087 € |
| EC max contribution | 1˙283˙087 € (100%) |
| Programme |
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC)) |
| Code Call | ERC-2014-CoG |
| Funding Scheme | ERC-COG |
| Starting year | 2015 |
| Duration (year-month-day) | from 2015-09-01 to 2020-08-31 |
Partnership
Take a look of project's partnership.
| # | ||||
|---|---|---|---|---|
| 1 | INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE | FR (LE CHESNAY CEDEX) | coordinator | 1˙283˙087.00 |
Map
Project objective
Efficient use of computational resources with a reliable outcome is a definite target in numerical simulations of partial differential equations (PDEs). Although this has been an important subject of numerical analysis and scientific computing for decades, still, surprisingly, often more than 90% of the CPU time in numerical simulations is literally wasted and the accuracy of the final outcome is not guaranteed. The reason is that addressing this complex issue rigorously is extremely challenging, as it stems from linking several rather disconnected domains like modeling, analysis of PDEs, numerical analysis, numerical linear algebra, and scientific computing. The goal of this project is to design novel inexact algebraic and linearization solvers, with each step being adaptively steered by optimal (guaranteed and robust) a posteriori error estimates, thus online interconnecting all parts of the numerical simulation of complex environmental porous media flows. The key novel ingredients will be multilevel algebraic solvers, tailored to porous media simulations, with problem- and discretization-dependent restriction, prolongation, and smoothing, yielding mass balance on all grid levels, accompanied by local adaptive stopping criteria. We shall theoretically prove the convergence of the new algorithms and justify their optimality, with in particular guaranteed (without any unknown constant) error reduction and overall computational load. Implementation into established numerical simulation codes and assessment on renowned academic and industrial benchmarks will consolidate the theoretical results. As a final outcome, the total simulation error will be certified and current computational burden cut by orders of magnitude. This would represent a cardinal technological advance both theoretically as well as practically in urgent environmental applications, namely the nuclear waste storage and the geological sequestration of CO2.
Publications
| year | authors and title | journal | last update |
|---|---|---|---|
| 2017 |
Ahmed , Elyes; Ali Hassan , Sarah; Japhet , Caroline; Kern , Michel; VohralÃk , Martin A posteriori error estimates and stopping criteria for space-time domain decomposition for two-phase flow between different rock types published pages: , ISSN: , DOI: |
HAL Preprints | 2019-05-31 |
| 2017 |
Alexandre Ern, Iain Smears, Martin VohralÃk Discrete p-robust $$varvec{H}({{mathrm{div}}})$$ H ( div ) -liftings and a posteriori estimates for elliptic problems with $$H^{-1}$$ H - 1 source terms published pages: 1009-1025, ISSN: 0008-0624, DOI: 10.1007/s10092-017-0217-4 |
Calcolo 54/3 | 2019-05-31 |
| 2017 |
Papež , Jan; Rüde , Ulrich; VohralÃk , Martin; Wohlmuth , Barbara Sharp algebraic and total a posteriori error bounds for $h$ and $p$ finite elements via a multilevel approach published pages: , ISSN: , DOI: |
HAL Preprints | 2019-05-31 |
| 2018 |
Málek, Josef; VohralÃk, Martin; Blechta, Jan Localization of the $W^{-1,q}$ norm for local a posteriori efficiency published pages: , ISSN: , DOI: |
HAL Preprints | 2019-05-31 |
| 2017 |
Dabaghi , Jad; Martin , Vincent; VohralÃk , Martin Adaptive inexact semismooth Newton methods for the contact problem between two membranes published pages: , ISSN: , DOI: |
HAL Preprints | 2019-05-31 |
| 2017 |
Alexandre Ern, Iain Smears, Martin VohralÃk Guaranteed, Locally Space-Time Efficient, and Polynomial-Degree Robust a Posteriori Error Estimates for High-Order Discretizations of Parabolic Problems published pages: 2811-2834, ISSN: 0036-1429, DOI: 10.1137/16M1097626 |
SIAM Journal on Numerical Analysis 55/6 | 2019-05-31 |
| 2018 |
Patrik Daniel, Alexandre Ern, Iain Smears, Martin VohralÃk An adaptive h p -refinement strategy with computable guaranteed bound on the error reduction factor published pages: 967-983, ISSN: 0898-1221, DOI: 10.1016/j.camwa.2018.05.034 |
Computers & Mathematics with Applications 76/5 | 2019-05-31 |
| 2016 |
Ern, Alexandre; VohralÃk, Martin; DolejÅ¡Ã, VÃt hp-adaptation driven by polynomial-degree-robust a posteriori error estimates for elliptic problems published pages: A3220–A3246, ISSN: 1064-8275, DOI: 10.1137/15M1026687 |
SIAM Journal on Scientific Computing 38/5 | 2019-05-31 |
| 2018 |
Sarah Ali Hassan, Caroline Japhet, Michel Kern, Martin VohralÃk A Posteriori Stopping Criteria for Optimized Schwarz Domain Decomposition Algorithms in Mixed Formulations published pages: 495-519, ISSN: 1609-4840, DOI: 10.1515/cmam-2018-0010 |
Computational Methods in Applied Mathematics 18/3 | 2019-05-31 |
| 2018 |
Martin VohralÃk, Soleiman Yousef A simple a posteriori estimate on general polytopal meshes with applications to complex porous media flows published pages: 728-760, ISSN: 0045-7825, DOI: 10.1016/j.cma.2017.11.027 |
Computer Methods in Applied Mechanics and Engineering 331 | 2019-05-31 |
| 2018 |
Patrick Ciarlet, Jr., Martin Vohralik Localization of global norms and robust a posteriori error control for transmission problems with sign-changing coefficients published pages: , ISSN: 0764-583X, DOI: 10.1051/m2an/2018034 |
ESAIM: Mathematical Modelling and Numerical Analysis | 2019-05-31 |
| 2018 |
VohralÃk, Martin; Ern, Alexandre Stable broken H1 and H(div) polynomial extensions for polynomial-degree-robust potential and flux reconstruction in three space dimensions published pages: , ISSN: , DOI: |
HAL Preprints | 2019-05-31 |
| 2018 |
Alexandre Ern, Iain Smears, Martin VohralÃk Equilibrated flux a posteriori error estimates in $L^2(H^1)$-norms for high-order discretizations of parabolic problems published pages: , ISSN: 0272-4979, DOI: 10.1093/imanum/dry035 |
IMA Journal of Numerical Analysis | 2019-05-31 |
| 2018 |
Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin VohralÃk Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework published pages: 1033-1079, ISSN: 0029-599X, DOI: 10.1007/s00211-018-0984-0 |
Numerische Mathematik 140/4 | 2019-05-31 |
| 2018 |
Sarah Ali Hassan, Caroline Japhet, Martin VohralÃk A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations published pages: 151-181, ISSN: 1068-9613, DOI: 10.1553/etna_vol49s151 |
ETNA - Electronic Transactions on Numerical Analysis 49 j | 2019-05-31 |
| 2018 |
Martin ÄŒermák, Frédéric Hecht, Zuqi Tang, Martin VohralÃk Adaptive inexact iterative algorithms based on polynomial-degree-robust a posteriori estimates for the Stokes problem published pages: 1027-1065, ISSN: 0029-599X, DOI: 10.1007/s00211-017-0925-3 |
Numerische Mathematik 138/4 | 2019-05-31 |
| 2018 |
J. Papež, Z. StrakoÅ¡, M. VohralÃk Estimating and localizing the algebraic and total numerical errors using flux reconstructions published pages: 681-721, ISSN: 0029-599X, DOI: 10.1007/s00211-017-0915-5 |
Numerische Mathematik 138/3 | 2019-05-31 |
| 2017 |
Eric Cancès, Geneviève Dusson, Yvon Maday, Benjamin Stamm, Martin VohralÃk Guaranteed and Robust a Posteriori Bounds for Laplace Eigenvalues and Eigenvectors: Conforming Approximations published pages: 2228-2254, ISSN: 0036-1429, DOI: 10.1137/15M1038633 |
SIAM Journal on Numerical Analysis 55/5 | 2019-05-31 |
| 2018 |
Cancès, Clément; Nabet, Flore; VohralÃk, Martin Convergence and a posteriori error analysis for energy-stable finite element approximations of degenerate parabolic equations published pages: , ISSN: , DOI: |
2019-04-18 | |
| 2018 |
Neumuller, Martin; Smears, Iain Time-parallel iterative solvers for parabolic evolution equations published pages: , ISSN: , DOI: |
2019-04-18 |
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