Hierarchical Data Structures and Algorithms for Computer Graphics. Part I.
IEEE Computer Graphics and Applications
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
An adaptively refined Cartesian mesh solver for the Euler equations
Journal of Computational Physics
Adaptive mesh refinement computation of solidification microstructures using dynamic data structures
Journal of Computational Physics
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Hierarchical Data Structures and Algorithms for Computer Graphics
IEEE Computer Graphics and Applications
Generalized barycentric coordinates on irregular polygons
Journal of Graphics Tools
Computer Aided Geometric Design
SuperLU Users'' Guide
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In this paper, the quadtree data structure and conforming polygonal interpolants are used to develop an h-adaptive finite element method. Quadtree is a hierarchical data structure that is computationally attractive for adaptive numerical simulations. Mesh generation and adaptive refinement of quadtree meshes is straight-forward. However, finite elements are non-conforming on quadtree meshes due to level-mismatches between adjacent elements, which results in the presence of so-called hanging nodes. In this study, we use meshfree (natural-neighbor, nn) basis functions on a reference element combined with an affine map to construct conforming approximations on quadtree meshes. Numerical examples are presented to demonstrate the accuracy and performance of the proposed h-adaptive finite element method.