Related papers: Benchmark of Polygon Quality Metrics for Polytopal…
This work delves into solving the two dimensional Poisson problem through the Finite Element Method which is relevant in various physical scenarios including heat conduction, electrostatics, gravity potential, and fluid dynamics. However,…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral equation techniques that allow for the efficient and accurate evaluation of quantities needed in…
In this paper we consider a coupled bulk-surface PDE in two space dimensions. The model consists of a PDE in the bulk that is coupled to another PDE on the surface through general nonlinear boundary conditions. For such a system we propose…
Microscopy images contain rich information about how cells respond to perturbations, making them essential to applications like drug screening. To quantify images, researchers often use representation extraction methods, and recent years…
We develop an all-hex meshing strategy for the interstitial space in beds of densely packed spheres that is tailored to turbulent flow simulations based on the spectral element method (SEM). The SEM achieves resolution through elevated…
The paper presents an assumed strain formulation over polygonal meshes to accurately evaluate the strain fields in nonlocal damage models. An assume strained technique based on the Hu-Washizu variational principle is employed to generate a…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
This paper presents an asymptotically compatible error bound for the finite element method (FEM) applied to a nonlocal diffusion model. The analysis covers two scenarios: meshes with and without shape regularity. For shape-regular meshes,…
A homogenization approach is one of effective strategies to solve multiscale elliptic problems approximately. The finite element heterogeneous multiscale method (FEHMM) which is based on the finite element makes possible to simulate such…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
We consider the isoparametric finite element method (FEM) for the Poisson equation in a smooth domain with the homogeneous Dirichlet boundary condition. Because the boundary is curved, standard triangulated meshes do not exactly fit it.…
A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper for the biharmonic equation in its primary form. This method is highly robust and flexible in the element construction by using discontinuous piecewise…
The Finite element method (FEM) has long served as the computational backbone for topology optimization (TO). However, for designing structures undergoing large deformations, conventional FEM-based TO often exhibits numerical instabilities…
Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
This work presents a Virtual Element Method (VEM) formulation tailored for two-dimensional axisymmetric problems in linear elasticity. By exploiting the rotational symmetry of the geometry and loading conditions, the problem is reduced to a…
The traditional display of elements in the periodic table is convenient for the study of chemistry and physics. However, the atomic number alone is insufficient for training statistical machine learning models to describe and extract…