Publications related to Spectral method

Spectral Estimators for High-Dimensional Matrix Inference

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

EPFL2024

An optimal preconditioned FFT-accelerated finite element solver for homogenization

Till Junge, Ali Falsafi, Martin Ladecký

We generalize and provide a linear algebra-based perspective on a finite element (FE) ho-mogenization scheme, pioneered by Schneider et al. (2017)[1] and Leuschner and Fritzen (2018)[2]. The efficiency of the scheme is based on a preconditioned, well-scale ...

ELSEVIER SCIENCE INC2023

Low-Rank Tensor Methods for High-Dimensional Problems

Christoph Max Strössner

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

EPFL2023

Geometrical Treatise on the Modelling of 3D Particulate Inclusion-Matrix Microstructures with an Application to Historical Stone Masonry Walls

Mahmoud S. M. Shaqfa

As historical stone masonry structures are vulnerable and prone to damage in earthquakes, investigating their structural integrity is important to reduce injuries and casualties while preserving their historical value. Stone masonry is a composite material ...

EPFL2022

Reduced 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 PHYSICS2022

Contact.engineering-Create, analyze and publish digital surface twins from topography measurements across many scales

Till Junge, Abhijeet Gujrati

The optimization of surface finish to improve performance, such as adhesion, friction, wear, fatigue life, or interfacial transport, occurs largely through trial and error, despite significant advancements in the relevant science. There are three central c ...

IOP Publishing Ltd2022

Fast global spectral methods for three-dimensional partial differential equations

Daniel Kressner, Christoph Max Strössner

Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...

OXFORD UNIV PRESS2022

Fourier Collocation and Reduced Basis Methods for Fast Modeling of Compressible Flows

Jan Sickmann Hesthaven, Deep Ray

A projection-based reduced order model (ROM) based on the Fourier collocation method is proposed for compressible flows. The incorporation of localized artificial viscosity model and filtering is pursued to enhance the robustness and accuracy of the ROM fo ...

GLOBAL SCIENCE PRESS2022

Controlling oscillations in spectral methods by local artificial viscosity governed by neural networks

Jan Sickmann Hesthaven, Deep Ray, Lukas Schwander

While a nonlinear viscosity is used widely to control oscillations when solving conservation laws using high-order elements based methods, such techniques are less straightforward to apply in global spectral methods since a local estimate of the solution r ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Construction of optimal spectral methods in phase retrieval

Florent Gérard Krzakala, Lenka Zdeborová

We consider the phase retrieval problem, in which the observer wishes to recover a n-dimensional real or complex signal X⋆ from the (possibly noisy) observation of |ΦX⋆|, in which Φ is a matrix of size m×n. We consider a \emph{high-dimensional} setting whe ...

2021

SiML: Sieved Maximum Likelihood for Array Signal Processing

Paul Hurley, Matthieu Martin Jean-André Simeoni

Stochastic Maximum Likelihood (SML) is a popular direction of arrival (DOA) estimation technique in array signal processing. It is a parametric method that jointly estimates signal and instrument noise by maximum likelihood, achieving excellent statistical ...

2021

Invariance principles in the theory and computation of transport coefficients

Federico Grasselli

In this work, we elaborate on two recently discovered invariance principles, according to which transport coefficients are, to a large extent, independent of the microscopic definition of the densities and currents of the conserved quantities being transpo ...

2021

Fourier uniqueness in even dimensions

Maryna Viazovska

In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness results in several key dimensions (d = 1, 8, 24), in which a function could be uniquely reconstructed from the values of it and its Fourier transform on a discr ...

National Academy of Sciences2021

Versatile shaping of optical frequency combs and applications

Jianqi Hu

Optical frequency combs are a series of phase-locked and equidistant laser lines in the spectral domain. In the time domain, they correspond to periodic pulse trains by the Fourier relation. The ability to shape optical combs and pulse trains is pivotal to ...

EPFL2021

Reduction techniques for PDEs built upon Reduced Basis and Domain Decomposition Methods with applications to hemodynamics

Luca Pegolotti

This thesis focuses on the development and validation of a reduced order technique for cardiovascular simulations. The method is based on the combined use of the Reduced Basis method and a Domain Decomposition approach and can be seen as a particular imple ...

EPFL2021

Hybrid asynchronous SEM/FEM co-simulation for seismic nonlinear analysis of concrete gravity dams

Nicolas Richart, Michael Ludovic Brun

The aim of this work is to take full advantage of Spectral Element (SE) and Finite Element (FE) codes by setting up a SEM/FEM co-simulation strategy for soil structure interaction problems, involving a SE code to generate and propagate elastic waves in the ...

PERGAMON-ELSEVIER SCIENCE LTD2021

Near-Field Mapping of Photonic Eigenmodes in Patterned Silicon Nanocavities by Electron Energy-Loss Spectroscopy

Duncan Thomas Lindsay Alexander, Valentin Flauraud

Recently, there has been significant interest in using dielectric nanocavities for the controlled scattering of light, owing to the diverse electromagnetic modes that they support. For plasmonic systems, electron energy-loss spectroscopy (EELS) is now an e ...

2021

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

Sparsely Observed Functional Time Series: Theory and Applications

Tomas Rubin

Functional time series is a temporally ordered sequence of not necessarily independent random curves. While the statistical analysis of such data has been traditionally carried out under the assumption of completely observed functional data, it may well ha ...

EPFL2021

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