Related papers: A tutorial-driven introduction to the parallel fin…

With deep learning models rapidly growing in size, systems-level solutions for large-model training are required. We present Amazon SageMaker model parallelism, a software library that integrates with PyTorch, and enables easy training of…

This paper introduces PolyDiM, an open-source C++ library tailored for the development and implementation of polytopal discretization methods for partial differential equations. The library provides robust and modular tools to support…

In order to learn distributed port-Hamiltonian systems (dPHS) using Gaussian processes (GPs), the partitioned finite element method (PFEM) is combined with the Gp-dPHS method. By following a late lumping approach, the discretization of the…

This note describes an extended exercise on the finite-element (FE) simulation of an accelerator magnet. The students construct and simulate a magnet model using the FEMM freeware. They get the opportunity to exercise on the theory of FEs,…

The take-home message of this paper is that solving optimal control problems can be computationally straightforward, provided that differentiable partial differential equation (PDE) solvers are available. Although this might seem to be a…

In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…

We consider a partial differential equation (PDE) model to predict residential burglary derived from a probabilistic agent-based model through a mean-field limit operation. The PDE model is a nonlinear, coupled system of two equations in…

This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson…

This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular…

This paper recalls the principles of the finite-element methods (FEM) theory and declines its application in the EN-MME group, for the numerical modelling and study of particle accelerator equipment. Implicit and explicit methods are…

Partial differential equations (PDEs) are used to describe a variety of physical phenomena. Often these equations do not have analytical solutions and numerical approximations are used instead. One of the common methods to solve PDEs is the…

Computational meshes, as a way to partition space, form the basis of much of PDE simulation technology, for instance for the finite element and finite volume discretization methods. In complex simulations, we are often driven to modify an…

Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be…

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…

Modelling complex physical systems through partial differential equations (PDEs) is central to many disciplines in science and engineering. Yet in most real applications, unknown or incomplete relationships such as constitutive or thermal…

A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the…

We present FooPar, an extension for highly efficient Parallel Computing in the multi-paradigm programming language Scala. Scala offers concise and clean syntax and integrates functional programming features. Our framework FooPar combines…

Approximating partial differential equations for extensive industrial and scientific applications requires leveraging the power of modern high-performance computing. In large-scale parallel computations, the geometrical discretisation…

The efficient solution of discretisations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been expended on scalable algorithms to precondition Krylov…