Related papers: Bringing Trimmed Serendipity Methods to Computatio…
One of the reasons for the success of the finite element method is its versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In the case of second order…
We consider families of finite elements on polygonal meshes, that are defined implicitly on each mesh cell as solutions of local Poisson problems with polynomial data. Functions in the local space on each mesh cell are evaluated via…
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…
High throughput first-principles calculations, based on solving the quantum mechanical many-body problem for hundreds of materials in parallel, have been successfully applied to advance many materials-based technologies, from batteries to…
Tree ensembles are powerful models that achieve excellent predictive performances, but can grow to unwieldy sizes. These ensembles are often post-processed (pruned) to reduce memory footprint and improve interpretability. We present…
Semiring algebras have been shown to provide a suitable language to formalize many noteworthy combinatorial problems. For instance, the Shortest-Path problem can be seen as a special case of the Algebraic-Path problem when applied to the…
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…
So-called "classification trimmed likelihood curves" have been proposed as a useful heuristic tool to determine the number of clusters and trimming proportion in trimming-based robust clustering methods. However, these curves needs a…
We consider, as a simple model problem, the application of Virtual Element Methods (VEM) to the linear Magnetostatic three-dimensional problem in the formulation of F. Kikuchi. In doing so, we also introduce new serendipity VEM spaces,…
The design, implementation and analysis of a free library for boundary element calculations is presented. The library is free in the sense of the GNU General Public Licence and is intended to allow users to solve a wide range of problems…
We propose two families of mixed finite elements for solving the classical Hellinger-Reissner mixed problem of the linear elasticity equations in three dimensions. First, a family of conforming mixed triangular prism elements is constructed…
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…
This article's main scope is the presentation of a computational method for the simulation of contact problems within the finite element method involving complex and rough surfaces. The approach relies on the MPJR (eMbedded Profile for…
Dot product kernels, such as polynomial and exponential (softmax) kernels, are among the most widely used kernels in machine learning, as they enable modeling the interactions between input features, which is crucial in applications like…
This work explores an extension of machine learning-optimized piecewise polynomial approximation by incorporating energy optimization as an additional objective. Traditional closed-form solutions enable continuity and approximation targets…
One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
We introduce a novel TRUNC finite element in n dimensions, encompassing the traditional TRUNC triangle as a particular instance. By establishing the weak continuity identity, we identify it as crucial for error estimate. This element is…
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…
1) We introduce random discrete Morse theory as a computational scheme to measure the complicatedness of a triangulation. The idea is to try to quantify the frequence of discrete Morse matchings with a certain number of critical cells. Our…