Towards a Compiler for Reals

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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 ...

Smart contracts have emerged as the most promising foundations for applications of the blockchain technology. Even though smart contracts are expected to serve as the backbone of the next-generation web, they have several limitations that hinder their wide ...

Situational awareness strategies are essential for the reliable and secure operation of the electric power grid which represents critical infrastructure in modern society. With the rise of converter-interfaced renewable generation and the consequent shift ...

The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

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 ...

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Time-domain solutions of Maxwell’s equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are co ...

Literature on linear induction motors (LIMs) has proposed several approaches to model the behavior of such devices for different applications. In terms of accuracy and fidelity, field analysis-based models are the most relevant. Closed-form or numerical so ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

Purpose: This study aims to evaluate two distinct approaches for fiber radius estimation using diffusion-relaxation MRI data acquired in biomimetic microfiber phantoms that mimic hollow axons. The methods considered are the spherical mean power-law approac ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

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 ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

State-of-the-art Artificial Intelligence (AI) algorithms, such as graph neural networks and recommendation systems, require floating-point computation of very large matrix multiplications over sparse data. Their execution in resource-constrained scenarios, ...

Compute memories are memory arrays augmented with dedicated logic to support arithmetic. They support the efficient execution of data-centric computing patterns, such as those characterizing Artificial Intelligence (AI) algorithms. These architectures can ...

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

Background: Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors ...

Towards a Compiler for Reals

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

Towards General-Purpose Decentralized Computing with Permissionless Extensibility

Functional-Basis Analysis of Non-Stationary Signals in Modern Power Grids: Theory and Implementation in Embedded Systems

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

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

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

The time-domain Cartesian multipole expansion of electromagnetic fields

Pseudo-Three-Dimensional Analytical Model of Linear Induction Motors for High-Speed Applications

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Pore size estimation in axon-mimicking microfibers with diffusion-relaxation MRI

From low-rank retractions to dynamical low-rank approximation and back

Error estimates for SUPG-stabilised Dynamical Low Rank Approximations

Stability: a search for structure

Randomized flexible GMRES with deflated restarting

Reliable data-driven decision-making through optimal transport

A 16-bit Floating-Point Near-SRAM Architecture for Low-power Sparse Matrix-Vector Multiplication

Overflow-free compute memories for edge AI acceleration

An equilibrated flux a posteriori error estimator for defeaturing problems

lifex-ep: a robust and efficient software for cardiac electrophysiology simulations