相关论文: A tetrahedral space-filling curve for non-conformi…
This article deals with solving partial differential equations with the finite element method on hybrid non-conforming hexahedral-tetrahedral meshes. By non-conforming, we mean that a quadrangular face of a hexahedron can be connected to…
In this thesis, we develop, discuss and implement algorithms for scalable parallel tree-based adaptive mesh refinement (AMR) using space-filling curves (SFCs). We create an AMR software that works independently of the used element type,…
The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not…
This paper is concerned with inserting three-dimensional computer-aided design (CAD) geometries into meshes composed of hexahedral elements using a volume fraction representation. An adaptive procedure for doing so is presented. The…
We propose an algorithm based on Hilbert space-filling curves to reorder mesh elements in memory for use with the Spectral Element Method, aiming to attain fewer cache misses, better locality of data reference and faster execution. We…
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.…
Two important classes of three-dimensional elements in computational meshes are hexahedra and tetrahedra. While several efficient methods exist that convert a hexahedral element to a tetrahedral elements, the existing algorithm for…
Convolutional neural networks (CNN) have been broadly studied on images, videos, graphs, and triangular meshes. However, it has seldom been studied on tetrahedral meshes. Given the merits of using volumetric meshes in applications like…
We present a cache-oblivious adaptation of matrix multiplication to be incorporated in the parallel TU decomposition for rectangular matrices over finite fields, based on the Morton-hybrid space-filling curve representation. To realise…
Adaptive mesh refinement is a key component of efficient unstructured space-time finite element methods. Underlying any adaptive mesh refinement scheme is, of course, a method for local refinement of simplices. However, simplex bisection…
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…
A tetrahedral curve is a space curve whose defining ideal is an intersection of powers of monomial prime ideals of height two. It is supported on a tetrahedral configuration of lines. Schwartau described when certain such curves are ACM,…
3D shape representations that accommodate learning-based 3D reconstruction are an open problem in machine learning and computer graphics. Previous work on neural 3D reconstruction demonstrated benefits, but also limitations, of point cloud,…
Applications that require Internet access to remote 3D datasets are often limited by the storage costs of 3D models. Several compression methods are available to address these limits for objects represented by triangle meshes. Many CAD and…
Space-filling curves like the Hilbert-curve, Peano-curve and Z-order map natural or real numbers from a two or higher dimensional space to a one dimensional space preserving locality. They have numerous applications like search structures,…
This paper presents efficient data structures for the implementation of matrix-free finite element methods on block-structured, hybrid tetrahedral grids. It provides a complete categorization of all geometric sub-objects that emerge from…
We advertise the use of tetrahedral grids constructed via the longest edge bisection algorithm for rendering volumetric data with path tracing. The key benefits of such grids is two-fold. First, they provide a highly adaptive…
In this paper a local Fourier analysis for multigrid methods on tetrahedral grids is presented. Different smoothers for the discretization of the Laplace operator by linear finite elements on such grids are analyzed. A four-color smoother…
Finite elements of higher continuity, say conforming in $H^2$ instead of $H^1$, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to…
In this paper we introduce three complementary three-dimensional weighted quadratic enrichment strategies to improve the accuracy of local histopolation on tetrahedral meshes. The first combines face and interior weighted moments…