Related papers: A structure-exploiting numbering algorithm for fin…
We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted graded meshes…
This paper proposes an efficient FDTD technique for determining electromagnetic fields interacting with a finite-sized 2D and 3D periodic structures. The technique combines periodic boundary conditions---modelling fields away from the edges…
Despite decades of research in this area, mesh adaptation capabilities are still rarely found in numerical simulation software. We postulate that the primary reason for this is lack of usability. Integrating mesh adaptation into existing…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
Trimming consists of cutting away parts of a geometric domain, without reconstructing a global parametrization (meshing). It is a widely used operation in computer aided design, which generates meshes that are unfitted with the described…
We present a numerical method to model the dynamics of inextensible biomembranes in a quasi-Newtonian incompressible flow, which better describes hemorheology in the small vasculature. We consider a level set model for the fluid-membrane…
The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by…
Recovered finite element methods (R-FEM) have been recently introduced for meshes consisting of simplicial and/or box-type meshes. Here, utilising the flexibility of R-FEM framework, we extend their definition on polygonal and polyhedral…
This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…
We introduce the concept of data-driven finite element methods. These are finite-element discretizations of partial differential equations (PDEs) that resolve quantities of interest with striking accuracy, regardless of the underlying mesh…
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…
Data compression plays a key role in reducing storage and I/O costs. Traditional lossy methods primarily target data on rectilinear grids and cannot leverage the spatial coherence in unstructured mesh data, leading to suboptimal compression…
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…
The computational efficiency of the Finite-Difference Time-Domain (FDTD) method can be significantly reduced by the presence of complex objects with fine features. Small geometrical details impose a fine mesh and a reduced time step,…
We present a finite element modelling approach for unidirectional Fused Filament Fabrication (FFF)-printed specimens under tensile loading. In this study, the focus is on the fracture behaviour, the goal is to simulate the mechanical…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…
We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that evolves inside/"on top" of it. Here the overlapping mesh is prescribed a simple discontinuous…
We present a simple yet general and efficient approach to representation of computational meshes. Meshes are represented as sets of mesh entities of different topological dimensions and their incidence relations. We discuss a…
The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…
We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…