Related papers: Local Element Operations for Curved Simplex Meshes
In the present paper, an integrated paradigm for topology optimization on complex surfaces with arbitrary genus is proposed. The approach is constructed based on the two-dimensional (2D) Moving Morphable Component (MMC) framework, where a…
Accurately solving PDEs with localised features requires refined meshes that adapt to the solution. Traditional numerical methods, such as finite elements, are linear in nature and often ineffective for such problems, as the mesh is not…
We consider the problem of global optimization of an unknown non-convex smooth function with zeroth-order feedback. In this setup, an algorithm is allowed to adaptively query the underlying function at different locations and receives noisy…
This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…
In this paper we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the…
This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
High-order partial differential equations (PDEs) require derivative regularity that standard $C^0$ finite element infrastructures do not directly provide on unstructured meshes. We propose a mesh-intrinsic generalized finite element method…
The convergence of multigrid methods degrades significantly if a small number of low quality cells are present in a finite element mesh, and this can be a barrier to the efficient and robust application of multigrid on complicated geometric…
An accurate implicit description of geometries is enabled by the level-set method. Level-set data is given at the nodes of a higher-order background mesh and the interpolated zero-level sets imply boundaries of the domain or interfaces…
We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance…
High-order finite element methods harbor the potential to deliver improved accuracy per degree of freedom versus low-order methods. Their success, however, hinges upon the use of a curvilinear mesh of not only sufficiently high accuracy but…
We devise and evaluate numerically a Hybrid High-Order (HHO) method for incremental associative plasticity with small deformations. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton,…
This paper introduces a new local plastic correction algorithm that is aimed at accelerating elasto-plastic finite element (FE) simulations for structural problems exhibiting localised plasticity (around e.g. notches, geometrical defects).…
In the past few years, following the differentiable programming paradigm, there has been a growing interest in computing the gradient information of physical processes (e.g., physical simulation, image rendering). However, such processes…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
Compatible schemes localize degrees of freedom according to the physical nature of the underlying fields and operate a clear distinction between topological laws and closure relations. For elliptic problems, the cornerstone in the scheme…
In mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex, the exterior derivative operators are computed exactly, so the spatial locality is preserved. However, the numerical approximations of the…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
In this paper, the stabilized finite element method based on local projection is applied to discretize the Stokes eigenvalue problems and the corresponding convergence analysis is given. Furthermore, we also use a method to improve the…