Unité
Chaire de mathématiques computationnelles et science de la simulation
LaboratoirePublications associées (214)
SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS
Simone Deparis, Riccardo Tenderini, Nicholas Mueller
In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...
Philadelphia2024Robust mass lumping and outlier removal strategies in isogeometric analysis
Annalisa Buffa, Espen Sande, Yannis Dirk Voet
Mass lumping techniques are commonly employed in explicit time integration schemes for problems in structural dynamics and both avoid solving costly linear systems with the consistent mass matrix and increase the critical time step. In isogeometric analysi ...
2024Shape 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 ...
2023High-order geometric integrators for the variational Gaussian approximation
Jiri Vanicek, Roya Moghaddasi Fereidani
Among the single-trajectory Gaussian-based methods for solving the time-dependent Schrödinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller’s original thawed Gaussian approximation, it is symplectic, conse ...
2023THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS
Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod
The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...
Philadelphia2023Structure-preserving approaches and data-driven closure modeling for model order reduction
In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...
EPFL2022Stabilized 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 ...
EPFL2022Reduced basis methods for numerical room acoustic simulations with parametrized boundaries
Jan Sickmann Hesthaven, Hermes Sampedro Llopis
The use of model-based numerical simulations of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively, which is computationally expensive. We present a reduced basis metho ...
ACOUSTICAL SOC AMER AMER INST PHYSICS2022Conservation of Forces and Total Work at the Interface Using the Internodes Method
The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...
2022