Related papers: T-IFISS: a toolbox for adaptive FEM computation
The development of data-driven approaches for solving differential equations has been followed by a plethora of applications in science and engineering across a multitude of disciplines and remains a central focus of active scientific…
SfePy (Simple finite elements in Python) is a software for solving various kinds of problems described by partial differential equations in one, two or three spatial dimensions by the finite element method. Its source code is mostly (85\%)…
Frequent Itemsets (FIs) mining is a fundamental primitive in data mining. It requires to identify all itemsets appearing in at least a fraction $\theta$ of a transactional dataset $\mathcal{D}$. Often though, the ultimate goal of mining…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…
This paper introduces the FEDM (Finite Element Discharge Modelling) code, which was developed using the open-source computing platform FEniCS (https://fenicsproject.org). Building on FEniCS, the FEDM code utilises the finite element method…
While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains $\Omega \subset \mathbb{R} ^d, $ $d=1,2,3$ in association with…
At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This…
Predictive systems, in particular machine learning algorithms, can take important, and sometimes legally binding, decisions about our everyday life. In most cases, however, these systems and decisions are neither regulated nor certified.…
In recent years, the immersed finite element methods (IFEM) introduced in \cite{Li2003}, \cite{Li2004} to solve elliptic problems having an interface in the domain due to the discontinuity of coefficients are getting more attentions of…
The focus of the tool FTOS is to alleviate designers' burden by offering code generation for non-functional aspects including fault-tolerance mechanisms. One crucial aspect in this context is to ensure that user-selected mechanisms for the…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
We present a method whereby the finite element method is used to train physics-informed neural networks that are suitable for surrogate modeling. The method is based on a custom convolutional operation called stencil convolution which…
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…
We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adaptive mesh-refinement with an energy-contractive linearization…
These lecture notes for a graduate course present an introduction to the mathematical theory of finite element methods for the numerical solution of partial differential equations. Covered are conforming and nonconforming (in particular,…
Current image segmentation techniques usually require that the user tune several parameters in order to obtain maximum segmentation accuracy, a computationally inefficient approach, especially when a large number of images must be processed…
Federated Learning (FL) has undergone significant development since its inception in 2016, advancing from basic algorithms to complex methodologies tailored to address diverse challenges and use cases. However, research and benchmarking of…
We present TopoTB, a software package written in the Mathematica language, designed to compute electronic structures, topological properties, and phase diagrams based on tight-binding models. TopoTB is user-friendly, with an interactive…
This work introduces a novel, fully robust and highly-scalable, $h$-adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method is based on a recent distributed-memory implementation of the…