Publications related to Poisson's equation

Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces

We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spa ...

OXFORD UNIV PRESS2023

Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques

Tobias Schneider, Omid Ashtari

Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solutions, their identification remains a computational challenge, rendering many ...

Cambridge University Press2023

A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods

Jiannong Fang

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 ...

2023

Adaptive analysis-aware defeaturing

Annalisa Buffa, Rafael Vazquez Hernandez, Ondine Gabrielle Chanon

Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. But depen ...

2022

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Riccardo Puppi

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 ...

EPFL2022

An a posteriori error estimator for isogeometric analysis on trimmed geometries

Annalisa Buffa, Rafael Vazquez Hernandez, Ondine Gabrielle Chanon

Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer-aided design, which generates meshes that are unfitted with the described physical object. T ...

2022

Piecewise linear interface-capturing volume-of-fluid method in axisymmetric cylindrical coordinates

Andreas Pautz, Lubomír Bures, Yohei Sato

The paper describes a novel implementation of the piecewise linear interface-capturing volume-of-fluid method (PLIC-VOF) in axisymmetric cylindrical coordinates. The principal innovative feature involved in this work is that both the forward and inverse re ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach

Annalisa Buffa, Pablo Antolin Sanchez, Rafael Vazquez Hernandez, Luca Coradello

The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic partial differential equations defined on two-dimensiona ...

2020

Dynamics of optical forces and torques in plasmonic systems: a surface integral equation

Olivier Martin, Karim Achouri, Andrei Kiselev

A novel approach is introduced to determine the time evolution of optical forces and torques on arbitrary shape nanostructures by combining Maxwell's stress tensor with the surface integral equation method (SIE). Conventional time averaging of Maxwell’s st ...

SPIEDigitalLibrary2020

A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

Alfio Quarteroni, Ondine Gabrielle Chanon

In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods and NURBS-based Isogeometric Analysis in its basic form, that is in the framework of the Galerkin method, for the approximation of the Poisso ...

SPRINGER/PLENUM PUBLISHERS2020

Two-Dimensional RBF-ENO Method on Unstructured Grids

Jan Sickmann Hesthaven, Fabian Mönkeberg

Essentially non-oscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely used to solve partial differential equations with discontinuous solutions. However, stable ENO/WENO methods on unstructured grids are less well stud ...

SPRINGER/PLENUM PUBLISHERS2020

Discrete Helmholtz charge distribution at liquid-liquid interfaces: Electrocapillarity, capacitance and non-linear spectroscopy studies

Hubert Girault, Grégoire Clément Gschwend

The structure of the polarised interface between two immiscible electrolyte solutions (ITIES) has usually been deduced from electrocapillarity and capacitance measurements. However, these two methods only offer an indirect access to the surface change dens ...

ELSEVIER SCIENCE SA2020

High-Order Accurate Conservative Finite Difference Methods For Vlasov Equations In 2D+2V

Stephan Brunner

This manuscript discusses discretization of the Vlasov-Poisson system in 2D+2V phase space using high-order accurate conservative finite difference algorithms. One challenge confronting direct kinetic simulation is the significant computational cost associ ...

SIAM PUBLICATIONS2019

Modeling of fatigue behavior based on interaction between time- and cyclic-dependent mechanical properties

Thomas Keller, Anastasios Vassilopoulos

A general constitutive equation was established using the theory of viscoelasticity in order to consider the interaction of the time- and cyclic-dependent mechanical properties of laminated composites. This equation was solved for two specific loading patt ...

2019

On raw inertial measurements in dynamic networks

Jan Skaloud, Davide Antonio Cucci

Dynamic Networks have been introduced in the literature to solve multi-sensor fusion problems for navigation and mapping. They have been shown to outperform conventional methods in challenging scenarios, such as corridor mapping or self-calibration. In thi ...

2019

An Equation-Free Approach For Second Order Multiscale Hyperbolic Problems In Non-Divergence Form

Doghonay Arjmand

The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale behavior, hence t ...

INT PRESS BOSTON, INC2018

Origin of enhancement in Raman scattering from Ag-dressed carbon-nanotube antennas: experiment and modelling

Olivier Martin

The D- and G-band Raman signals from random arrays of vertically aligned, multi-walled carbon nanotubes are significantly enhanced (up to ∼14×) while the signal from the underlying Si substrate is simultaneously attenuated (up to ∼6×) when the nanotubes ar ...

2018

Multi space reduced basis preconditioners for parametrized partial differential equations

Niccolò Dal Santo

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

EPFL2018

Silencing the second harmonic generation from plasmonic nanodimers: A comprehensive discussion

Olivier Martin, Jérémy Butet, Gabriel David Bernasconi

The silencing of the second harmonic generation process from plasmonic nanostructures corresponds to the limited far-field second harmonic radiation despite the huge fundamental electric field enhancement in the interstice between two plasmonic nanoparticl ...

BEILSTEIN-INSTITUT2018

Tailoring the field enhancement in Fano-resonant nanoantennas for improved optical bistability

Olivier Martin, Jérémy Butet

The influence of Fano resonances on the nonlinear response of hybrid plasmonic nanostructures, i.e., nanoantennas loaded with a nonlinear optical material, is theoretically investigated using the combination of a surface integral equation method and an ana ...

2017