A unified analysis for conforming and nonconforming stabilized finite element methods using interior penalty

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Immersed boundary-conformal isogeometric method for linear elliptic problems

Annalisa Buffa, Pablo Antolin Sanchez, Xiaodong Wei

We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this manner, we leverage t ...

2021

Fabrication, Characterization, and Simulation of Glass Devices with AlN Thin-Film Transducers for Excitation of Ultrasound Resonances

Paul Muralt, Ramin Matloub Aghdam

We present the fabrication of 570-mu m-thick millimeter-sized soda-lime-silicate float-glass blocks with a 1-mu m-thick AlN thin-film piezoelectric transducer sandwiched between thin metallic electrodes and deposited on the top surface. The electromechanic ...

American Physical Society (APS)2021

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin

We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021

Hemodynamics of the heart's left atrium based on a Variational Multiscale-LES numerical method

Alfio Quarteroni, Filippo Menghini

In this paper, we investigate the haemodynamics of a left atrium (LA) by proposing a computational model suitable to provide physically meaningful fluid dynamics indications and detailed blood flow characterization. In particular, we consider the incompres ...

ELSEVIER2021

Improving parametric mass modelling of lensing clusters through a perturbative approach

Jean-Paul Richard Kneib, Benjamin Yvan Alexandre Clement, Benjamin Emmanuel Nicolas Beauchesne

We present a new method to model the mass distribution of galaxy clusters that combines a parametric and a free-form approach to reconstruct cluster cores with strong lensing constraints. It aims at combining the advantages of both approaches, by keeping t ...

OXFORD UNIV PRESS2021

Model order reduction of flow based on a modular geometrical approximation of blood vessels

Simone Deparis, Luca Pegolotti

We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier–Stokes equations. Our algorithm is based on an approximated domain-decomposition of the ...

2021

On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

Tommaso Vanzan

The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a p ...

Springer-Verlag2023

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

The equivalent pier method for energy pile groups

Lyesse Laloui, Alessandro Francesco Rotta Loria

This study presents a method for estimating the average vertical displacement of energy pile groups subjected to thermal loads. The method consists of replacing any regular energy pile group with a single equivalent pier of the same length and an equivalen ...

2017

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...

Siam Publications2013