Related papers: Code generation for generally mapped finite elemen…
We address multiscale elliptic problems with random coefficients that are a perturbation of multiscale deterministic problems. Our approach consists in taking benefit of the perturbative context to suitably modify the classical Finite…
We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in…
We consider a saddle point formulation for a sixth order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet-Raviart formulation for the biharmonic problem to…
Irksome is a library based on the Unified Form Language (UFL) that enables automated generation of Runge--Kutta methods for time-stepping finite element spatial discretizations of partial differential equations (PDE). Allowing users to…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
We consider the numerical approximation of a continuum model of antiferromagnetic and ferrimagnetic materials. The state of the material is described in terms of two unit-length vector fields, which can be interpreted as the magnetizations…
In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under…
We examine the effect of using complexity-reducing relations to generate optimized code for the evaluation of finite element variational forms. The optimizations are implemented in a prototype code named FErari, which has been integrated as…
The main purpose of this article is to facilitate the implementation of space-time finite element methods in four-dimensional space. In order to develop a finite element method in this setting, it is necessary to create a numerical…
The scalar wave equation is solved using higher order immersed finite elements. We demonstrate that higher order convergence can be obtained. Small cuts with the background mesh are stabilized by adding penalty terms to the weak…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…
Large-scale 3D martensitic microstructure evolution problems are studied using a finite-element discretization of a finite-strain phase-field model. The model admits an arbitrary crystallography of transformation and arbitrary elastic…
We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of…
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy…
This work introduces a hybrid approach that combines the Proper Generalised Decomposition (PGD) with deep learning techniques to provide real-time solutions for parametrised mechanics problems. By relying on a tensor decomposition, the…
Modeling the unusual mechanical properties of metamaterials is a challenging topic for the mechanics community and enriched continuum theories are promising computational tools for such materials. The so-called relaxed micromorphic model…
Two de Rham complex sequences of the finite element spaces are introduced for weak finite element functions and weak derivatives developed in the weak Galerkin (WG) finite element methods on general polyhedral elements. One of the sequences…
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…
A novel method for performing model updating on finite element models is presented. The approach is particularly tailored to modal analyses of buildings, by which the lowest frequencies, obtained by using sensors and system identification…