Related papers: High-performance finite elements with MFEM
Many classical and modern finite element spaces are derived by dividing each computational cell into finer pieces. Such \emph{macroelements} frequently enable the enforcement of mathematically desirable properties such as divergence-free…
Medusa, a novel library for implementation of strong form mesh-free methods, is described. We identify and present common parts and patterns among many such methods reported in the literature, such as node positioning, stencil selection and…
The paper presents the project of an open source C/C++ library of analytical solutions to micromechanical fields within media with ellipsoidal heterogeneities. The solutions are based on Eshelby's stress-free, in general polynomial,…
The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…
Recent hardware acceleration advances have enabled powerful specialized accelerators for finite element computations, spiking neural network inference, and sparse tensor operations. However, existing approaches face fundamental limitations:…
Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this…
Identifying anomalies has become one of the primary strategies towards security and protection procedures in computer networks. In this context, machine learning-based methods emerge as an elegant solution to identify such scenarios and…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…
To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…
Reservoir simulators utilize numerical techniques to solve the governing equations of fluid flow in porous media and they are essential tool for oil and gas fields development. In practical reservoir simulation, the finite difference method…
We have developed a finite-element micromagnetic simulation code based on the FEniCS package called magnum.fe. Here we describe the numerical methods that are applied as well as their implementation with FEniCS. We apply a transformation…
The widespread success of foundation models in natural language processing and computer vision has inspired researchers to extend the concept to scientific machine learning and computational science. However, this position paper argues that…
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac…
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,…
The $hp$-adaptive finite element method (FEM) - where one independently chooses the mesh size ($h$) and polynomial degree ($p$) to be used on each cell - has long been known to have better theoretical convergence properties than either $h$-…
Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…
Recent feature matching methods have achieved remarkable performance but lack efficiency consideration. In this paper, we revisit the mainstream detector-free matching pipeline and improve all its stages considering both accuracy and…
Cracking Elements Method (CEM) is a numerical tool to simulate quasi-brittle fractures, which does not need remeshing, nodal enrichment, or complicated crack tracking strategy. The cracking elements used in the CEM can be considered as a…
Deformable fractured porous media appear in many geoscience applications. While the extended finite element (XFEM) has been successfully developed within the computational mechanics community for accurate modeling of the deformation, its…
This paper reviews standard oversampling strategies as performed in the Multiscale Finite Element Method (MsFEM). Common to those approaches is that the oversampling is performed in the full space restricted to a patch but including coarse…