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. Fields of science natural sciencesmathematicspure mathematicsalgebralinear algebranatural sciencescomputer and information sciencescomputational sciencenatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicsapplied mathematicsnumerical analysisnatural sciencesmathematicsapplied mathematicsmathematical model Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-CoG-2014 - ERC Consolidator Grant Call for proposal ERC-2014-CoG See other projects for this call Funding Scheme ERC-COG - Consolidator Grant Coordinator INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE Net EU contribution € 1 283 087,50 Address Domaine de voluceau rocquencourt 78153 Le chesnay cedex France See on map Region Ile-de-France Ile-de-France Yvelines Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET AUTOMATIQUE France Net EU contribution € 1 283 087,50 Address Domaine de voluceau rocquencourt 78153 Le chesnay cedex See on map Region Ile-de-France Ile-de-France Yvelines Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
