2021-03680 - Post-Doctoral Research Visit F/M Adaptive linearization for nonlinear numerical PDEs

Contract type : Fixed-term contract

Renewable contract : Oui

Level of qualifications required : PhD or equivalent

Fonction : Post-Doctoral Research Visit

Context

Context

The post-doc project inscribes into the continuity of the European Research Council (ERC) Consolidator Grant GATIPOR Guaranteed fully adaptive algorithms with tailored inexact solvers for complex porous media flowshttps://project.inria.fr/gatipor/ (ends August 2021). This project studied algorithms for numerical approximation of complex systems of unsteady nonlinear partial differential equations arising in underground porous media problems. It aimed at designing novel inexact algebraic and linearization solvers, with each step being adaptively steered, interconnecting at any time all parts of the numerical simulation algorithm. Its key ingredient were optimal a posteriori estimates on the error in the approximate solution which give a guaranteed global upper bound and which distinguish the different error components like the spatial, temporal, regularization, linearization, and algebraic solver ones. It included computer implementation, assessment on academic and industrial benchmarks, and applications to contemporary environmental problems like underground storage of dangerous waste or geological sequestration of CO2.

Within the framework 

Assignment

Goal

The recruited person is supposed to work on numerical discretizations of nonlinear partial differential equations (PDEs). The goal will be to design novel adaptive approaches combining different linearization techniques like the Picard or L-schemes with the Netwon method.

References and links

A state of the art, bibliography, and scientific references are available at the following URL: https://project.inria.fr/gatipor/publications/ and https://project.inria.fr/gatipor/news/.

Responsibilities

The person recruited will be responsible for theoretical developments and their computer implementation.

Main activities

  • Devise an adaptive linearization, where the initial iterations are performed by a widely-converging linearization scheme (Picard- or L-scheme-type) whereas the later iterations are performed by a fast-converging linearization scheme (Newton)-type.
  • Desing a switch steered by a posteriori error estimates.
  • Design an adaptive inexact linearization extension, where the linear system associated with the given linearization (Newton/Pickard/L-scheme) is not solved exactly but only approximated by an iterative algebraic solver with a stopping criterion again steered by a posteriori error estimates.
  • Provide rigorous analysis for model problems and heuristic extensions for more complex applications.
  • Provide computer implementation.
  • Consider applications to porous media flows.

Skills

Ph.D. in numerical analysis and scientific computing (finite element methods, linearization methods (Picard, Newton, L-scheme), multigrid/domain decomposition algebraic solvers), strong publication record, programming skills (C, C++, Matlab).

Benefits package

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage