Related papers: Fast variable density node generation on parametri…
This work describes a concise algorithm for the generation of triangular meshes with the help of standard adaptive finite element methods. We demonstrate that a generic adaptive finite element solver can be repurposed into a triangular mesh…
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…
In this paper, we study a numerical method for the solution of partial differential equations on evolving surfaces. The numerical method is built on the stabilized trace finite element method (TraceFEM) for the spatial discretization and…
Subsampling of node sets is useful in contexts such as multilevel methods, computer graphics, and machine learning. On uniform grid-based node sets, the process of subsampling is simple. However, on node sets with high density variation,…
The development of higher order finite elements methods has become an active research area. The deformation method for mesh generation has achieved a prescribed positive Jacobian determinant constraint and it has been a useful method for…
Due to the limit of mesh density, the improvement of the spatial precision of numerical computation always leads to a decrease in computing efficiency. Aiming at this inability of numerical computation, we propose a novel method for…
Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…
During a surface acquisition process using 3D scanners, noise is inevitable and an important step in geometry processing is to remove these noise components from these surfaces (given as points-set or triangulated mesh). The noise-removal…
We present an optimization procedure for generic polygonal or polyhedral meshes, tailored for the Virtual Element Method (VEM). Once the local quality of the mesh elements is analyzed through a quality indicator specific to the VEM, groups…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
This study presents a meshfree two-dimensional fractional-order Element-Free Galerkin (2D f-EFG) method as a viable alternative to conventional mesh-based FEM for a numerical solution of (spatial) fractional-order differential equations…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
Mesh generation plays a crucial role in scientific computing. Traditional mesh generation methods, such as TFI and PDE-based methods, often struggle to achieve a balance between efficiency and mesh quality. To address this challenge,…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…
This paper describes a node relocation algorithm based on nonlinear optimization which delivers excellent results for both unstructured and structured plane triangle meshes over convex as well as non-convex domains with high curvature. The…
Computational Fluid Dynamics (CFD) is widely used in different engineering fields, but accurate simulations are dependent upon proper meshing of the simulation domain. While highly refined meshes may ensure precision, they come with high…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The method uses a Poisson disk sampling-type technique for coarsening…