Martin Vohralík

Directeur de recherche Inria Vědecký pracovník, Inria Senior researcher at Inria
Equipe-projet SERENA, responsable Projekt SERENA, vedoucí Project-team SERENA, team leader
martin.vohralik@inria.fr
photo

Inria Paris Inria Paris Inria Paris

2 rue Simone Iff
75589 Paris
France
&

CERMICS, ENPC CERMICS, ENPC CERMICS, ENPC

Université Paris-Est
6 et 8, av. Blaise Pascal
77455 Marne-la-Vallée
France

French Czech English



Thèmes de recherche Výzkumné zájmy Research topics

  • discrétisations numériques des équations aux dérivées partielles
  • estimations d'erreur a posteriori (fiabilité de l'intégralité de la procédure de simulation numérique)
  • adaptivité (utilisation efficace des ressources, y compris des solveurs algébriques et de linéarisation itératifs)
  • simulations numériques (écoulements et transport de contaminants en milieux poreux)
  • numerické diskretizace parciálních diferenciálních rovnic
  • a posteriorní odhady chyb (zaručení kvality výsledku numerické simulace)
  • adaptivita (efektivní využití výpočetních prostředků, včetně iteračních algebraických řešičů a iterativní linearizace)
  • numerické simulace (proudění a transport kontaminantů v porézním prostředí)
  • numerical discretizations of partial differential equations
  • a posteriori error estimates (reliability of the overall simulation process)
  • adaptivity (efficient use of computational resources, including iterative algebraic solvers and iterative linearization)
  • numerical simulations (flow and transport of contaminants in porous media)

Bref CV Stručný životopis Express CV

Enseignement Výuka Teaching

Estimations d'erreur a posteriori, Sorbonne Université, Paris (2012–15) & Université Charles, Prague (2012–)
Ecoles d'été / d'hiver
A posteriorní odhady chyb, Univerzita Sorbonne, Paříž (2012–15) & Univerzita Karlova, Praha (2012–)
Letní / zimní Školy
A posteriori error estimates, Sorbonne University, Paris (2012–15) & Charles University, Prague (2012–)
Summer/winter schools

Projets de recherche Výzkumné projekty Research Projects

GATIPOR (ERC consolidator grant, PI, 2015–2020)
DEDALES (ANR, 2014–18)
GEOPOR (ANR, 2013–17)
MoRe (ERC-CZ, gouv. R. tchèque, co-PI, 2012–17)
GATIPOR (ERC consolidator grant, PI, 2015–2020)
DEDALES (Fr. grantová agentura, 2014–18)
GEOPOR (Fr. grantová agentura, 2013–17)
MoRe (ERC-CZ, vláda České rep., co-PI, 2012–17)
GATIPOR (ERC consolidator grant, PI, 2015–2020)
DEDALES (Fr. Nat. Research Agency, 2014–18)
GEOPOR (Fr. Nat. Research Agency, 2013–17)
MoRe (ERC-CZ, Czech R. gov., co-PI, 2012–17)

Comités de rédaction Redakční rady Editorial boards

Acta Polytechnica (2009–)
Applications of Mathematics (2018–)
SIAM Journal on Numerical Analysis (2013–2019)

Comités de conférences Komise konferencí Conference committees

ENUMATH (2013, 15, 17, scientifique)
Finite Volumes for Complex Applications (2011, 14, 17, scientifique et d'organisation) Presentation of Mathematics (2010, 12, 14, scientifique)
SimRace (2015, 19, scientifique)
ENUMATH (2013, 15, 17, vědecká)
Finite Volumes for Complex Applications (2011, 14, 17, vědecká a organizační) Presentation of Mathematics (2010, 12, 14, vědecká)
SimRace (2015, 19, vědecká)
ENUMATH (2013, 15, 17, scientific)
Finite Volumes for Complex Applications (2011, 14, 17, scientific and organizing) Presentation of Mathematics (2010, 12, 14, scientific)
SimRace (2015, 19, scientific)

Quelques résultats récents Několik nových výsledků Some recent results

Localisation des normes W-1,q et de distance Lokalizace W-1,q a vzdálenostní normy Localization of the W-1,q and distance norms
localization
  • dual norm of any bounded linear functional on the Sobolev space W01,p localizes under an orthogonality condition: equals the lq sum of local contributions;
  • estimates taking into account the violation of the orthogonality condition;
  • distance to the Sobolev space H01 localizes: equals the l2 sum of local contributions (no orthogonality condition);
  • implies local efficiency and robustness of a posteriori estimates for nonlinear and non-coercive partial differential equations in divergence form;
  • includes the case of inexact solvers;
  • H01 setting including nonconformity: paper with Patrick Ciarlet, Jr., presentation;
  • W01,p setting: paper with Jan Blechta and Josef Málek, presentation.
Equivalence local-global, projection et approximation hp dans H(div) Ekvivalence lokální - globální, projekce a hp aproximace v H(div) Local-global equivalence, projection, and hp approximation in H(div)
local_global
  • global-best approximation (constraints on normal component continuity and divergence) is equivalent to the sum of independent local-best approximations (no constraints);
  • gives rise to a simple stable local commuting projector in H(div);
  • this projector delivers approximation error equivalent to the local-best approximation;
  • leads to optimal hp approximation estimates in H(div);
  • applies under the minimal necessary Sobolev regularity;
  • gives optimal a priori hp-error estimates for mixed and least-squares finite element methods;
  • preprint with Alexandre Ern, Thirupathi Gudi, and Iain Smears, presentation.
Maillages polytopaux et écoulements complexes en milieux poreux Polytopální sítě a komplexní proudění v porézním prostředí Polytopal meshes and complex porous media flows
polyt
  • general polytopal meshes;
  • easy-to-implement and fast-to-run a posteriori error estimates given by a simple matrix–vector multiplication;
  • works for any lowest-order locally conservative method, extends to higher-order;
  • guaranteed upper bound on the total error;
  • distinction of different error components (spatial discretization, temporal discretization, linearization, algebraic solver);
  • unsteady nonlinear coupled degenerate problems (multiphase multicomponent flows in porous media);
  • paper with Soleiman Yousef, presentation.

Plus dans la galerie GATIPOR Více v galerii GATIPOR More in the GATIPOR gallery


Logiciels Programy Codes


Thésards Doktorandi Ph.D. students

Ani Miraci (2017–)
Jad Dabaghi (2015–2019)
Patrik Daniel (2015–2019)
Sarah Ali Hassan (2013–2017)
Soleiman Yousef (2009–2013)
Carole Heinry (2009–2013)
Nancy Chalhoub (2008–2012)

Post-docs Post-doktorandi Post-docs

Kenan Kergrene (2018–)
Jan Papež (2019)
Mohammad Zakerzadeh (2017–2019)
Gouranga Mallik (2017–2018)
Iain Smears (2015–2017)
Zuqi Tang (2013–2015)

Equipe SERENA Projekt SERENA SERENA team

SERENA


organization

personal