Michele Botti

Michele Botti
Politecnico di Milano | Polimi · Department of Mathematics "Francesco Brioschi"

Postdoctoral researcher
Design and analysis of polyhedral discretization methods for geomechanical modeling

About

36
Publications
2,728
Reads
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278
Citations
Citations since 2016
35 Research Items
278 Citations
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20162017201820192020202120220204060
20162017201820192020202120220204060
20162017201820192020202120220204060
Introduction
Since March 2019, I work as research fellow at MOX. I am ER of the PDGeoFF project, funded by the EU in the context of MSCA-IF. The aim of the project is to develop a numerical framework to evaluate risks related to human geological activities. I have completed my PhD at the University of Montpellier in 2018. The thesis focused on the development of advanced discretization methods for poromechanical simulation. The PhD research work was conjointly funded by the BRGM and LabEx NUMEV.
Additional affiliations
March 2019 - November 2020
Politecnico di Milano
Position
  • PostDoc Position
Description
  • Researcher in Applied Mathematics and Engineering: Advanced Discretization Methods for Geomechanical Simulation
Education
October 2015 - November 2018
Université de Montpellier
Field of study
  • Mathematics
September 2013 - September 2015
University of Pavia
Field of study
  • Applied mathematics
October 2010 - September 2013
University of Pavia
Field of study
  • Mathematics

Publications

Publications (36)
Article
Full-text available
In this work we review discontinuous Galerkin finite element methods on polytopal grids (PolydG) for the numerical simulation of multiphysics wave propagation phenomena in heterogeneous media. In particular, we address wave phenomena in elastic, poro-elastic, and poro-elasto-acoustic materials. Wave propagation is modeled by using either the elasto...
Preprint
Full-text available
In this work we address the reduction of face degrees of freedom (DOFs) for discrete elasticity complexes. Specifically, using serendipity techniques, we develop a reduced version of a recently introduced two-dimensional complex arising from traces of the three-dimensional elasticity complex. The keystone of the reduction process is a new estimate...
Preprint
In this work, we present an uncertainty quantification analysis to determine the influence and importance of some physical parameters in a reactive transport model in fractured porous media. An accurate description of flow and transport in the fractures is key to obtain reliable simulations, however, fractures geometry and physical characteristics...
Presentation
Full-text available
Advanced Numerical Methods for Scientific Computing (NuMeth) group
Presentation
Full-text available
Presentation given at ECCOMAS 2022 - MS 25: Robust and Reliable methods for poromechanics
Preprint
Full-text available
We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal and polyhedral grids based on a novel four-field formulation of the problem. To handle the non-linear convect...
Article
The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by the acoustics equations in the acoustic domain and the low-frequency Biot's equations in the poroelastic one....
Presentation
Full-text available
In this talk, we focus on the numerical analysis of a polyhedral discontinuous Galerkin (PolyDG) scheme for the numerical simulation of multiphysics wave propagation in heterogeneous media. In particular, we address wave phenomena in poro-elasto-acoustic materials modeled by coupling the low-frequency Biot’s equations and the acoustics equations. T...
Preprint
In this work we review discontinuous Galerkin finite element methods on polytopal grids (PolydG) for the numerical simulation of multiphysics wave propagation phenomena in heterogeneous media. In particular, we address wave phenomena in elastic, poro-elastic, and poro-elasto-acoustic materials. Wave propagation is modeled by using either the elasto...
Article
Full-text available
In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of conver...
Presentation
Full-text available
In this talk, we focus on the numerical analysis of a polyhedral discontinuous Galerkin (PolyDG) scheme for the poroelasto-acoustic differential problem modeling an acoustic wave impacting a poroelastic medium and consequently propagating through it. Coupled poroelasto-acoustic models find application in many science and engineering fields, e.g., i...
Presentation
Full-text available
We design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed discretization hinges on discontinuous polynomial unknowns on the mesh and on its skeleton, from which discrete differential operators are reconstructed. The reco...
Chapter
We develop Hybrid High-Order methods for multiple-network poroelasticity, modelling seepage through deformable fissured porous media. The proposed methods are designed to support general polygonal and polyhedral elements. This is a crucial feature in geological modelling, where the need for general elements arises, e.g., due to the presence of frac...
Presentation
Full-text available
The presentation focuses on the numerical analysis of nonconforming monolithic discretizations of multiple-network poroelasticity problems, modeling seepage through deformable fissured media. The proposed schemes are based on Hybrid High-Order and discontinuous Galerkin methods and are designed to support general polyhedral elements. This is a veri...
Preprint
The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by the acoustics equations in the acoustic domain and the low-frequency Biot's equations in the poroelastic one....
Article
In this work, we introduce a novel abstract framework for the stability and convergence analysis of fully coupled discretisations of the poroelasticity problem and apply it to the analysis of Hybrid High-Order (HHO) schemes. A relevant feature of the proposed framework is that it rests on mild time regularity assumptions that can be derived from an...
Preprint
Full-text available
In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of conver...
Preprint
We develop Hybrid High-Order methods for multiple-network poroelasticity, modelling seepage through deformable fissured porous media. The proposed methods are designed to support general polygonal and polyhedral elements. This is a crucial feature in geological modelling, where the need for general elements arises, e.g., due to the presence of frac...
Preprint
Full-text available
In this work, we introduce a novel abstract framework for the stability and convergence analysis of fully coupled discretisations of the poroelasticity problem and apply it to the analysis of Hybrid High-Order (HHO) schemes. A relevant feature of the proposed framework is that it rests on mild time regularity assumptions that can be derived from an...
Article
In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the stochastic partial differential system and establish its well-posedness. We then discuss the approximation of the par...
Presentation
Full-text available
We consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modeled using a finite set of parameters with prescribed probability distribution. The well-posedness of the variational formulation of the stochastic partial differential system is established . We carry out an in-depth study of the dependence between the phys...
Article
In this work, we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darc...
Preprint
Full-text available
In this work we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darcy...
Article
Full-text available
In this work we construct a low-order nonconforming approximation method for linear elasticity problems supporting general meshes and valid in two and three space dimensions. The method is obtained by hacking the Hybrid High-Order method of Di Pietro and Ern (2015), that requires the use of polynomials of degree $k ≥ 1$ for stability. Specifically,...
Poster
Full-text available
We propose a novel numerical method for the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed distribution. We present the variational formulation of the stochastic partial differential system and establish its well-posedness. The approximation is based on sparse spect...
Preprint
In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the stochastic partial differential system and establish its well-posedness. We then discuss the approximation of the par...
Preprint
Full-text available
In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the stochastic partial differential system and establish its wellposedness. We then discuss the approximation of the para...
Preprint
Full-text available
In this work we construct a low-order nonconforming approximation method for linear elasticity problems supporting general meshes and valid in two and three space dimensions. The method is obtained by hacking the Hybrid High-Order method, that requires the use of polynomials of degree $k\ge1$ for stability. Specifically, we show that coercivity can...
Thesis
Full-text available
In this manuscript we focus on novel discretization schemes for solving the coupled equations of poroelasticity and we present analytical and numerical results for poromechanics problems relevant to geoscience applications. We propose to solve these problems using Hybrid High-Order (HHO) methods, a new class of nonconforming high-order methods supp...
Preprint
In this work, we construct and analyze a nonconforming high-order discretization method for the quasi-static single-phase nonlinear poroelasticity problem describing Darcean flow in a deformable porous medium saturated by a slightly compressible fluid. The nonlinear elasticity operator is discretized using a Hybrid High-Order method, while the Darc...
Article
Full-text available
We consider hyperelastic problems and their numerical solution using a conforming finite element discretization and iterative linearization algorithms. For these problems, we present equilibrated, weakly symmetric, $H(\rm{div)}$-conforming stress tensor reconstructions, obtained from local problems on patches around vertices using the Arnold--Falk-...
Article
Full-text available
In this work we propose and analyze a novel Hybrid High-Order discretization of a class of (linear and) nonlinear elasticity models in the small deformation regime which are of common use in solid mechanics. The proposed method is valid in two and three space dimensions, it supports general meshes including polyhedral elements and nonmatching inter...
Conference Paper
Full-text available
In this work, we introduce a novel algorithm for the quasi-static nonlinear poroelasticity problem describing Darcian flow in a deformable saturated porous medium. The nonlinear elasticity operator is discretized using a Hybrid High-Order method while the heterogeneous diffusion part relies on a Symmetric Weighted Interior Penalty discontinuous Gal...
Article
Full-text available
In this work, we introduce a novel algorithm for the Biot problem based on a Hybrid High-Order discretization of the mechanics and a Symmetric Weighted Interior Penalty discretization of the flow. The method has several assets, including, in particular, the support of general polyhedral meshes and arbitrary space approximation order. Our analysis d...

Network

Cited By
    • The Chinese University of Hong Kong
    • École des Ponts ParisTech
    • Indian Institute of Space Science and Technology
    • Ecole Nationale Supérieure d’Electrotechnique, d’Electronique, d’Informatique, d’Hydraulique et des Télécommunications
    • SINTEF Digital, Oslo, Norway

Projects

Projects (3)
Project
The PDGeoFF project, funded by the EU in the context of MSCA International Fellowships, will develop a mathematical and numerical framework to evaluate and prevent risks related to several human geological activities like geothermal energy production and CO2 storage. The research will target the investigation of the models describing fault mechanics and the interaction between propagating fractures and fluid flow. “The project leading to this application has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 896616.”
Project
Novel applications of the HHO methods for fluid and solid mechanics
Archived project
Development and analysis of high-order nonconforming discretization schemes for poroelasticity problems. Numerical investigation on a complete panel of two- and three-dimensional test cases in the context of geomechanics.