Publication
Global continuation for ODE systems over the half-line and study of von Kármán's swirling flow problem
Publications associées (91)
Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps
Jan Sickmann Hesthaven, Niccolo' Discacciati
We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...
Lausanne2024Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs
Fernando José Henriquez Barraza
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...
New York2024A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods
To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equ ...
2023Reduced order models for coupled systems
Efficient numerical simulations of coupled multi-component systems can be particularly challenging. This is mostly due to the complexity of their solutions, as mutual interactions may cause emergent behaviors, including synchronization and instabilities. V ...
EPFL2023Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds
Le Chen, Cheuk Yin Lee, David Jean-Michel Candil
We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...
New York2023Data-driven finite-thickness cohesive elements for frictional interfaces
Jean-François Molinari, Antonio Joaquin Garcia Suarez, Sacha Zenon Wattel, Yannick André Neypatraiky
Model-free data-driven computational mechanics (DDCM) [Kirchdoerfer & Ortiz, 2016] is a new paradigm for simulations in solid mechanics. As in the classical method, the boundary value problem is formulated with physics-based PDEs such as the balance of mom ...
2023Graphical solutions to one-phase free boundary problems
Xavier Fernandez-Real Girona, Hui Yu
We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient di ...
Berlin2023Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow
Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...
EPFL2022Microscale hydrodynamic confinements: shaping liquids across length scales as a toolbox in life sciences
Philippe Renaud, David Philipp Taylor, Prerit Mathur
Hydrodynamic phenomena can be leveraged to confine a range of biological and chemical species without needing physical walls. In this review, we list methods for the generation and manipulation of microfluidic hydrodynamic confinements in free-flowing liqu ...
ROYAL SOC CHEMISTRY2022Two mixed finite element formulations for the weak imposition of the Neumann boundary conditions for the Darcy flow
We propose two different discrete formulations for the weak imposition of the Neumann boundary conditions of the Darcy flow. The Raviart-Thomas mixed finite element on both triangular and quadrilateral meshes is considered for both methods. One is a consis ...
2021