Related papers: Element-Saving Hexahedral 3-Refinement Templates
This work is related to PHG (Parallel Hierarchical Grid). PHG is a toolbox for developing parallel adaptive finite element programs, which is under active development at the State Key Laboratory of Scientific and Engineering Computing. The…
In this paper, we present an efficient adaptive multigrid strategy for the geometry optimization of large-scale three dimensional molecular mechanics. The resulting method can achieve significantly reduced complexity by exploiting the…
In this work we formally derive and prove the correctness of the algorithms and data structures in a parallel, distributed-memory, generic finite element framework that supports h-adaptivity on computational domains represented as…
Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its…
Highly accurate simulation of plasma transport is needed for the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers…
The forest-of-refinement-trees approach allows for dynamic adaptive mesh refinement (AMR) at negligible cost. While originally developed for quadrilateral and hexahedral elements, previous work established the theory and algorithms for…
This paper aims to develop an efficient adaptive finite element method for the second-order elliptic problem. Although the theory for adaptive finite element methods based on residual-type a posteriori error estimator and bisection…
This article is concerned with the numerical solution of convex variational problems. More precisely, we develop an iterative minimisation technique which allows for the successive enrichment of an underlying discrete approximation space in…
This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…
3D Gaussian Splatting (3DGS) has recently emerged as a promising 3D representation. Much research has been focused on reducing its storage requirements and memory footprint. However, the needs to compress and transmit the 3DGS…
In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…
This paper provides a simple, compact and efficient 90-line pedagogical MATLAB code for topology optimization using hexagonal elements (honeycomb tessellation). Hexagonal elements provide nonsingular connectivity between two juxtaposed…
This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…
The development of new manufacturing techniques such as 3D printing have enabled the creation of previously infeasible chemical reactor designs. Systematically optimizing the highly parameterized geometries involved in these new classes of…
In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…
In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these…
We study a model of programmable matter systems consisting of $n$ devices lying on a 2-dimensional square grid, which are able to perform the minimal mechanical operation of rotating around each other. The goal is to transform an initial…
We present an adaptive variational procedure for unstructured meshes to capture fluid-fluid interfaces in two-phase flows. The two phases are modeled by the phase-field finite element formulation, which involves the conservative Allen-Cahn…
In this paper we generalize to non-uniform grids of quad-tree type the Compact WENO reconstruction of Levy, Puppo and Russo (SIAM J. Sci. Comput., 2001), thus obtaining a truly two-dimensional non-oscillatory third order reconstruction with…
This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms…