Publications related to Round-off error

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

Walter De Gruyter Gmbh2024

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Paride Passelli

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

EPFL2024

Error estimates for SUPG-stabilised Dynamical Low Rank Approximations

Fabio Nobile, Thomas Simon Spencer Trigo Trindade

We perform an error analysis of a fully discretised Streamline Upwind Petrov Galerkin Dynamical Low Rank (SUPG-DLR) method for random time-dependent advection-dominated problems. The time integration scheme has a splitting-like nature, allowing for potenti ...

Springer Nature Switzerland2025

A mixed precision LOBPCG algorithm

Daniel Kressner, Meiyue Shao, Yuxin Ma

The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work, we propose a mix ...

SPRINGER2023

Assessing real-world gait with digital technology? Validation, insights and recommendations from the Mobilise-D consortium

Kamiar Aminian, Anisoara Ionescu, Abolfazl Soltani, Francesca Salis

Background: Although digital mobility outcomes (DMOs) can be readily calculated from real-world data collected with wearable devices and ad-hoc algorithms, technical validation is still required. The aim of this paper is to comparatively assess and validat ...

BioMed Central2023

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Daniel Kressner, Ivana Sain Glibic

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

SPRINGER2023

Bed Topography Inference from Velocity Field Using Deep Learning

Christophe Ancey, Mehrdad Kiani Oshtorjani

Measuring bathymetry has always been a major scientific and technological challenge. In this work, we used a deep learning technique for inferring bathymetry from the depth-averaged velocity field. The training of the neural network is based on 5742 labora ...

2023

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

Understanding motor control and impairment: An upper-limb model for muscular assessment

Tristan Jean Robin Barjavel

The human upper limb is a complex musculoskeletal system that can still perform various tasks with impressive efficacy thanks to the ability of the central nervous system to control and modulate the activation of more than 40 muscles. Stroke is a leading ...

EPFL2023

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

Validation of spectral simulation tools in the context of ipRGC-influenced light responses of building occupants

Marilyne Andersen, Clotilde Marie A Pierson

With the growing awareness about ipRGC-influenced light (IIL) responses, design applications related to these responses are flourishing. To compare design options and optimize lighting conditions for building occupants, lighting simulations are typically u ...

2023

Tumor control and radiobiological fingerprint after Gamma Knife radiosurgery for posterior fossa meningiomas: A series of 46 consecutive cases

Constantin Tuleasca

Introduction: Gamma Knife radiosurgery (GKR) can be a valuable treatment option for posterior cranial fossa meningiomas (PCFM). We retrospectively analyzed outcomes of GKR for PCFM.& nbsp;Methods: Were included forty-six patients with 47 PCFM. Primary endp ...

2022

Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a cont ...

2021

A parabolic local problem with exponential decay of the resonance error for numerical homogenization

Assyr Abdulle, Doghonay Arjmand, Edoardo Paganoni

This paper aims at an accurate and efficient computation of effective quantities, e.g. the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a m ...

WORLD SCIENTIFIC PUBL CO PTE LTD2021

LOD-Homogenization of Multiscale Eddy Current Problem in Time Domain

Yves Perriard, Xiaotao Ren

Devices fabricated from Soft Magnetic Composites (SMCs) are gaining popularity in research and application. The multiscale characteristics require special attention. Solving the quasi-statics Maxwell’s equations on such devices consumes huge time and memor ...

Institute of Electrical and Electronics Engineers2021

A probabilistic finite element method based on random meshes: A posteriori error estimators and Bayesian inverse problems

Assyr Abdulle, Giacomo Garegnani

We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows to introduce a pr ...

ELSEVIER SCIENCE SA2021

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Giacomo Garegnani

In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...

EPFL2021

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

Jiri Vanicek, Seonghoon Choi

Diabatization of the molecular Hamiltonian is a standard approach to remove the singularities of nonadiabatic couplings at conical intersections of adiabatic potential energy surfaces. In general, it is impossible to eliminate the nonadiabatic couplings en ...

2021

Reaching mK-scale stability in CP-ɸOTDR over daily measurements

Luc Thévenaz, Tiago Filipe Pimentel Das Neves, Luis Costa

We propose several processing methods to mitigate the probability of large errors in Chirped-pulse ɸOTDR, improving performances for long-term measurements. For no perturbation applied, we reach a 2 mK error after a 24 h experiment. ...

2020