Related papers: Finite Element Theory for PHIMATS
The combination of Finite Element Method (FEM) simulation and experimental photo-elasticity provides both qualitative and quantitative information about the stress field in a polymer composite and particularly along the fibre-matrix…
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…
Finite Element Analysis (FEA) serves as the cornerstone of modern engineering design. However, its workflow is inherently complex and relies heavily on domain expertise. Although recent efforts have integrated Large Language Models (LLMs)…
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…
We propose an efficient and accurate parametric finite element method (PFEM) for solving sharp-interface continuum models for solid-state dewetting of thin films with anisotropic surface energies. The governing equations of the…
FEMPAR is an open source object oriented Fortran200X scientific software library for the high-performance scalable simulation of complex multiphysics problems governed by partial differential equations at large scales, by exploiting…
This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
FIAT (the FInite element Automatic Tabulator) provides a powerful Python library for the generation and evaluation of finite element basis functions on a reference element. This release paper describes recent improvements to FIAT aimed at…
The numerical solution of partial differential equations using the finite element method is one of the key applications of high performance computing. Local assembly is its characteristic operation. This entails the execution of a…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting. To this end, we formulate an adaptive algorithm which steers…
In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive…
A general approach to simulate the mechanical behavior of textile materials by taking into account all their constitutive elementary fibers and contacts between them is presented in this paper. A finite element code, based on an implicit…
Many classical finite elements such as the Argyris and Bell elements have long been absent from high-level PDE software. Building on recent theoretical work, we describe how to implement very general finite element transformations in FInAT…
We present a projection-based numerical integration technique to deal with embedded interface in finite element (FE) framework. The element cut by an embedded interface is denoted as a cut cell. We recognize elemental matrices of a cut cell…
This review gives an overview of effective field theory (EFT) as applied at finite density, with a focus on nuclear many-body systems. Uniform systems with short-range interactions illustrate the ingredients and virtues of many-body EFT and…