Related papers: Optimal Dual Schemes for Adaptive Grid Based Hexme…
Conforming hexahedral (hex) meshes are favored in simulation for their superior numerical properties, yet automatically decomposing a general 3D volume into a conforming hex mesh remains a formidable challenge. Among existing approaches,…
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 describes a novel method of generating hex-dominant meshes using pre-computed optimal subdivisions of the unit cube in a grid-based approach. Our method addresses geometries that are standard in mechanical engineering and often…
This paper tackles the challenging problem of constrained hexahedral meshing. An algorithm is introduced to build combinatorial hexahedral meshes whose boundary facets exactly match a given quadrangulation of the topological sphere. This…
This work introduces an adaptive mesh refinement technique for hierarchical hybrid grids with the goal to reach scalability and maintain excellent performance on massively parallel computer systems. On the block structured hierarchical…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
Second order accurate Cartesian grid methods have been well developed for interface problems in the literature. However, it is challenging to develop third or higher order accurate methods for problems with curved interfaces and internal…
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…
Grids are a general representation for capturing regularly-spaced information, but since they are uniform in space, they cannot dynamically allocate resolution to regions with varying levels of detail. There has been some exploration of…
Standard PolyCube-based hexahedral (hex) meshing methods aim to deform the input domain into an axis-aligned PolyCube volume with integer corners; if this deformation is bijective, then applying the inverse map to the voxelized PolyCube…
In this article, we provide a detailed survey of techniques for hexahedral mesh generation. We cover the whole spectrum of alternative approaches to mesh generation, as well as post processing algorithms for connectivity editing and mesh…
This paper presents a novel algorithmic framework for the computational design, simulation, and fabrication of a hexagonal grid-based double-curvature structure with planar hexagonal panels. The journey begins with constructing a robust…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
Constructing well-behaved Laplacian and mass matrices is essential for tetrahedral mesh processing. Unfortunately, the \emph{de facto} standard linear finite elements exhibit bias on tetrahedralized regular grids, motivating the development…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…
Indirect hex-dominant meshing methods rely on the detection of adjacent tetrahedra an algorithm that performs this identification and builds the set of all possible combinations of tetrahedral elements of an input mesh T into hexahedra,…
Hexahedral (hex) meshing is a long studied topic in geometry processing with many fascinating and challenging associated problems. Hex meshes vary in complexity from structured to unstructured depending on application or domain of interest.…
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…
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…