Related papers: MFEM: a modular finite element methods library

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…

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…

Numerical simulations are ubiquitous in mathematics and computational science. Several industrial and clinical applications entail modeling complex multiphysics systems that evolve over a variety of spatial and temporal scales. This study…

We describe different optimization techniques to perform the assembly of finite element matrices in Matlab and Octave, from the standard approach to recent vectorized ones, without any low level language used. We finally obtain a simple and…

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…

The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…

This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented…

OpenGM is a C++ template library for defining discrete graphical models and performing inference on these models, using a wide range of state-of-the-art algorithms. No restrictions are imposed on the factor graph to allow for higher-order…

DefElement is an online encyclopedia of finite element definitions that was created and is maintained by the authors of this paper. DefElement aims to make information about elements defined in the literature easily available in a standard…

In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…

Scientific visualization tools tend to be flexible in some ways (e.g., for exploring isovalues) while restricted in other ways, such as working only on regular grids, or only on unstructured meshes (as used in the finite element method,…

We design a finite element method (FEM) for a membrane model of liquid crystal polymer networks (LCNs). This model consists of a minimization problem of a non-convex stretching energy. We discuss properties of this energy functional such as…

The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…

We present ensmallen, a fast and flexible C++ library for mathematical optimization of arbitrary user-supplied functions, which can be applied to many machine learning problems. Several types of optimizations are supported, including…

In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…

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…

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…

In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…

Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…

This report provides an introduction to the ensmallen numerical optimization library, as well as a deep dive into the technical details of how it works. The library provides a fast and flexible C++ framework for mathematical optimization of…