Related papers: FIAT: enabling classical and modern macroelements
Micromechanical homogenization is often carried out with Fourier-accelerated methods that are prone to ringing artifacts. We here generalize the compatibility projection introduced by Vond\v{r}ejc, Zeman & Marek [Comput. Math. Appl. 68, 156…
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…
Within the finite element community, discontinuous Galerkin (DG) and mixed finite element methods have become increasingly popular in simulating geophysical flows. However, robust and efficient solvers for the resulting saddle-point and…
We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free…
Fine-grained object detection in challenging visual domains, such as vehicle damage assessment, presents a formidable challenge even for human experts to resolve reliably. While DiffusionDet has advanced the state-of-the-art through…
In research labs, there is often a need to customise software at every step in a given bioinformatics workflow, but traditionally it has been difficult to obtain both a high degree of customisability and good performance.…
The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…
Today, interest in automotive applications notably Hybrid Electric Vehicles (HEV) has risen due to environmental concerns and the modern society's energetic dependence. Consequently, it is necessary to study and implement in these vehicle…
Complex mechatronic systems are typically composed of interconnected modules, often developed by independent teams. This development process challenges the verification of system specifications before all modules are integrated. To address…
In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional…
Semantic segmentation involves assigning a specific category to each pixel in an image. While Vision Transformer-based models have made significant progress, current semantic segmentation methods often struggle with precise predictions in…
In this paper we consider a spatially flat Friedmann-Robertson-Walker (FRW) cosmological model whit cosmological constant, containing a stiff fluid and a classical Dirac field. The proposed cosmological scenario describes the evolution of…
We study the fatigue fracture of disordered materials by means of computer simulations of a discrete element model. We extend a two-dimensional fracture model to capture the microscopic mechanisms relevant for fatigue, and we simulate the…
In this paper, we introduce the locally conservative enriched immersed finite element method (EIFEM) to tackle the elliptic problem with interface. The immersed finite element is useful for handling interface with mesh unfit with the…
This paper introduces discrete differential form spaces over two-dimensional manifold meshes that feature enhanced subdivision-induced inter-element regularity compared to conventional finite element (FE) spaces. This increase in smoothness…
The aim of the FESCA workshop is to bring together junior researchers from formal methods, software engineering, and industry interested in the development and application of formal modelling approaches as well as associated analysis and…
We present a novel phase-field model development capability in the open source MOOSE finite element framework. This facility is based on the 'modular free energy' approach in which the phase-field equations are implemented in a general form…
Modern order and lattice theory provides convenient mathematical tools for pattern mining, in particular for condensed irredundant representations of pattern spaces and their efficient generation. Formal Concept Analysis (FCA) offers a…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…