A5065838227- Advanced Numerical Methods in Computational Mathematics
- Advanced Mathematical Modeling in Engineering
- Numerical methods in engineering
- Groundwater flow and contamination studies
- Electromagnetic Simulation and Numerical Methods
- Computational Fluid Dynamics and Aerodynamics
- Differential Equations and Numerical Methods
- Contact Mechanics and Variational Inequalities
- Hydraulic Fracturing and Reservoir Analysis
- Electromagnetic Scattering and Analysis
- Lattice Boltzmann Simulation Studies
- Model Reduction and Neural Networks
- Elasticity and Material Modeling
- Numerical methods for differential equations
- Advanced Numerical Analysis Techniques
- Numerical methods in inverse problems
- Stability and Controllability of Differential Equations
- Reservoir Engineering and Simulation Methods
- Fluid Dynamics Simulations and Interactions
- Cellular Mechanics and Interactions
- Advanced Algebra and Geometry
- Wind and Air Flow Studies
- Topological and Geometric Data Analysis
- 3D Printing in Biomedical Research
- Fire dynamics and safety research
Politecnico di Milano
2022-2025
NORCE Norwegian Research Centre
2024
KTH Royal Institute of Technology
2017-2022
Universidad Adventista de Chile
2021
Simula Research Laboratory
2021
University of Oslo
2021
Monash University
2021
Sechenov University
2021
University of Stuttgart
2019-2020
University of Bergen
2015-2018
Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose new discretization, based on mixed finite element method mortar methods. Our formulation is novel that it employs normal fluxes as variable within framework, resulting couples flow fractures with surrounding domain strong notion of mass conservation. The proposed handles complex, nonmatching grids allows fracture intersections termination...
In this paper, we introduce a mortar-based approach to discretizing flow in fractured porous media, which term the mixed-dimensional flux coupling scheme. Our formulation is agnostic discretizations used discretize fluid equations medium and fractures, as such it represents unified integrated geometries into any existing discretization framework. particular, several approaches for media can be seen special instances of proposed herein. We provide an abstract stability theory our approach,...
Abstract We are interested in differential forms on mixed-dimensional geometries, the sense of a domain containing sets d -dimensional manifolds, structured hierarchically so that each manifold is contained boundary one or more $$d + 1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> manifolds. On any given manifold, we then consider operators tangent to as well discrete (jumps) normal...
We develop robust solvers for a class of perturbed saddle-point problems arising in the study second-order elliptic equation mixed form (in terms flux and potential), four-field formulation Biot's consolidation problem linear poroelasticity (using displacement, filtration flux, total pressure, fluid pressure). The stability continuous variational problems, which hinges upon using adequately weighted spaces, is addressed detail; efficacy proposed preconditioners, as well their robustness with...
Abstract We combine classical continuum mechanics with the recently developed calculus for mixed-dimensional problems to obtain governing equations flow in, and deformation of, fractured materials. present models in both context of finite infinitesimal strain, discuss nonlinear (and non-differentiable) constitutive laws such as friction contact fracture. Using theory well-posedness evolutionary maximal monotone operators, we show model case strain under certain assumptions on parameters.
We construct mesh-independent and parameter-robust monolithic solvers for the coupled primal Stokes--Darcy problem. Three different formulations their discretizations in terms of conforming nonconforming finite element methods volume are considered. In each case, robust preconditioners derived using a unified theoretical framework. particular, suggested utilize operators fractional Sobolev spaces. Numerical experiments demonstrate parameter-robustness proposed solvers.
Abstract A solution technique is proposed for flows in porous media that guarantees local conservation of mass. We first compute a flux field to balance the mass source and then exploit exact co-chain complexes generate solenoidal correction. reduced basis method based on proper orthogonal decomposition employed construct correction we show ensured regardless quality approximation. The directly applicable mixed finite virtual element methods, among other structure-preserving discretization...
We consider the equilibrium equations for a linearized Cosserat material. identify their structure in terms of differential complex, which is isomorphic to six copies de Rham complex through an algebraic isomorphism. Moreover, we show how materials can be analyzed by inheriting results from elasticity. Both perspectives give rise mixed finite element methods, refer as strongly and weaky coupled, respectively. prove convergence both classes with particular attention improved rate estimates,...
.This work proposes a mixed finite element method for the Biot poroelasticity equations that employs lowest-order Raviart–Thomas space solid displacement and piecewise constants fluid pressure. The is based on formulation of linearized elasticity as weighted vector Laplace problem. By introducing rotation flux auxiliary variables, we form four-field system, which discretized using conforming spaces. variables are subsequently removed from system in local hybridization technique to obtain...
This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and generalize regular decomposition to this setting. With use conforming mixed finite element spaces, we then expand these results discrete case obtain a in terms Lagrange elements. In turn, are proposed analogous Hiptmair Xu [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509]. Numerical experiments show performance...
In order to model the contractive forces exerted by fibroblast cells in dermal tissue, we propose and analyze two modeling approaches under assumption of linearized elasticity. The first approach introduces a collection point on boundary whereas second employs an isotropic stress source its center. We resulting partial differential equations terms weighted Sobolev spaces identify singular behavior respective solutions. Two finite element method are proposed, one based direct application...