Related papers: Computational Tools in EN-MME: Implicit and Explic…
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…
We describe in this work the numerical treatment of the Filament Based Lamellipodium Model (FBLM). The model itself is a two-phase two-dimensional continuum model, describing the dynamics of two interacting families of locally parallel…
We consider a randomised implementation of the finite element method (FEM) for elliptic partial differential equations on high-dimensional models. This is motivated by applications where model predictions are essential for real-time process…
The phase field model is a widely used mathematical approach for describing crack propagation in continuum damage fractures. In the context of phase field fracture simulations, adaptive finite element methods (AFEM) are often employed to…
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…
The state of the art in electromagnetic Finite Element Particle-in-Cell (EM-FEMPIC) has advanced significantly in the last few years. These have included understanding function spaces that must be used to represent sources and fields…
This work is devoted to design and study efficient and accurate numerical schemes to approximate a chemo-attraction model with consumption effects, which is a nonlinear parabolic system for two variables; the cell density and the…
High level domain specific languages for the finite element method underpin high productivity programming environments for simulations based on partial differential equations (PDE) while employing automatic code generation to achieve high…
FEpX is a modeling framework for computing the elastoplastic deformations of polycrystalline solids. Using the framework, one can simulate the mechanical behavior of aggregates of crystals, referred to as virtual polycrystals, over large…
Cracking Elements Method (CEM) is a numerical tool to simulate quasi-brittle fractures, which does not need remeshing, nodal enrichment, or complicated crack tracking strategy. The cracking elements used in the CEM can be considered as a…
In this paper we develop the first fine-grained rounding error analysis of finite element (FE) cell kernels and assembly. The theory includes mixed-precision implementations and accounts for hardware-acceleration via matrix multiplication…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
We present a computational framework for modeling large-scale particle-laden flows in complex domains with the goal of enabling simulations in medical-image derived patient specific geometries. The framework is based on a volume-filtered…
Finding optimal solutions to combinatorial optimization problems is pivotal in both scientific and technological domains, within academic research and industrial applications. A considerable amount of effort has been invested in the…
The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps…
An introductory exposition of the virtual element method (VEM) is provided. The intent is to make this method more accessible to those unfamiliar with VEM. Familiarity with the finite element method for solving 2D linear elasticity problems…
The aim of this study was to check how efficient can be smoothed finite element method (FEM) for solution of the linear fracture mechanics problems. Accuracy of stress intensity factor (SIF) computation were investigated using three types…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging…