Related papers: High-performance finite elements with MFEM
MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and…
Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions which generate a specific discretization space, and next…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
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…
The Virtual Element Method (VEM) is an extension of the Finite Element Method (FEM) used for handling polytopal meshes. This paper provides a brief introduction to the VEM for a two-dimensional Laplacian problem. Additionally, it highlights…
In this paper we describe the research and development activities in the Center for Efficient Exascale Discretization within the US Exascale Computing Project, targeting state-of-the-art high-order finite-element algorithms for high-order…
The capacity to predict and control bioprocesses is perhaps one of the most important objectives of biotechnology. Computational simulation is an established methodology for the design and optimization of bioprocesses, where the finite…
Many problems in science and engineering can be rigorously recast into minimizing a suitable energy functional. We have been developing efficient and flexible solution strategies to tackle various minimization problems by employing finite…
In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…
The progression of scientific computing resources has enabled the numerical approximation of mathematical models describing complex physical phenomena. A significant portion of researcher time is typically dedicated to the development of…
Deep learning models typically use single-precision (FP32) floating point data types for representing activations and weights, but a slew of recent research work has shown that computations with reduced-precision data types (FP16, 16-bit…
Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel…
The $\ell$FEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces. The finite element matrix assemblies are based on MATLAB's paged operators and…
This document summarizes the main concepts of the finite element (FE) theory and constitutive relations as implemented in the open-source code phase-field multiphysics materials simulator PHIMATS https://github.com/ahcomat/PHIMATS. PHIMATS…