Related papers: SfePy - Write Your Own FE Application
Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we…
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on applications in computational mechanics and design optimization. We leverage Mat\'ern-type…
This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…
The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational…
rigidPy is a Python package that provides a set of tools necessary for studying rigidity and mechanical response in spring networks. It also includes suitable modules for generating new realizations of networks with applications in glassy…
We present a high order immersed finite element (IFE) method for solving the elliptic interface problem with interface-independent meshes. The IFE functions developed here satisfy the interface conditions exactly and they have optimal…
We introduce an enriched immersed finite element method for addressing interface problems characterized by general non-homogeneous jump conditions. Unlike many existing unfitted mesh methods, our approach incorporates a homogenization…
The scaled boundary finite element method (SBFEM) is capable of generating polyhedral elements with an arbitrary number of surfaces. This salient feature significantly alleviates the meshing burden being a bottleneck in the analysis…
This paper presents a technique for stress and fracture analysis by using the scaled boundary finite element method (SBFEM) with quadtree mesh of high-order elements. The cells of the quadtree mesh are modelled as scaled boundary polygons…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
We introduce Diddy, a collection of Python scripts for analyzing infinite discrete dynamical systems. The main focus is on generalized multidimensional shifts of finite type (SFTs). We show how Diddy can be used to easily define SFTs and…
We introduce FDApy, an open-source Python package for the analysis of functional data. The package provides tools for the representation of (multivariate) functional data defined on different dimensional domains and for functional data that…
This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…
Youpi stands for "YOUpi is your processing PIpeline". It is a portable, easy to use web application providing high level functionalities to perform data reduction on scientific FITS images. It is built on top of open source processing tools…
We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…
Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
Understanding and reasoning about physics is an important ability of intelligent agents. We develop the PHYRE benchmark for physical reasoning that contains a set of simple classical mechanics puzzles in a 2D physical environment. The…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…