Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems
Journal of Computational Physics
On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation
Journal of Computational Physics
The cost of balancing generalized quadtrees
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems
SIAM Journal on Numerical Analysis
Tree methods for moving interfaces
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Two A Posteriori Error Estimates for One-Dimensional Scalar Conservation Laws
SIAM Journal on Numerical Analysis
Resolution of high order WENO schemes for complicated flow structures
Journal of Computational Physics
Understanding the Shu–Osher Conservative Finite Difference Form
Journal of Scientific Computing
Local level set method in high dimension and codimension
Journal of Computational Physics
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
Journal of Computational Physics
Fifth-Order Weighted Power-ENO Schemes for Hamilton-Jacobi Equations
Journal of Scientific Computing
Detail-preserving fully-Eulerian interface tracking framework
ACM SIGGRAPH Asia 2010 papers
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We develop high order essentially non-oscillatory (ENO) schemes on non-uniform meshes based on generalized binary trees. The idea is to adopt an appropriate data structure which allows to communicate information easily between unstructured data structure and virtual uniform meshes. While the generalized binary trees as an unstructured data structure can store solution information efficiently if combined with a good adaptive strategy, virtual uniform meshes allow us to take advantage of many well-developed ENO numerical methods based on uniform meshes. Therefore, the ENO adaptive tree methods proposed here can leverage the merits from both tree structures and uniform meshes. Numerical examples demonstrate that the new method is efficient and accurate.