Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Multiresolution representation of data: a general framework
SIAM Journal on Numerical Analysis
Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I
SIAM Journal on Scientific Computing
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Multidimensional binary search trees used for associative searching
Communications of the ACM
Fully adaptive multiresolution finite volume schemes for conservation laws
Mathematics of Computation
A conservative fully adaptive multiresolution algorithm for parabolic PDEs
Journal of Computational Physics
Finite elements on dyadic grids with applications
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
An adaptive multiresolution scheme with local time stepping for evolutionary PDEs
Journal of Computational Physics
Adaptive Multiresolution Methods for the Simulation of Waves in Excitable Media
Journal of Scientific Computing
Hi-index | 7.29 |
We propose a modified adaptive multiresolution scheme for solving d-dimensional hyperbolic conservation laws which is based on cell-average discretization in dyadic grids. Adaptivity is obtained by interrupting the refinement at the locations where appropriate scale (wavelet) coefficients are sufficiently small. One important aspect of such a multiresolution representation is that we can use the same binary tree data structure for domains of any dimension. The tree structure allows us to succinctly represent the data and efficiently navigate through it. Dyadic grids also provide a more gradual refinement as compared with the traditional quad-trees (2D) or oct-trees (3D) that are commonly used for multiresolution analysis. We show some examples of adaptive binary tree representations, with significant savings in data storage when compared to quad-tree based schemes. As a test problem, we also consider this modified adaptive multiresolution method, using a dynamic binary tree data structure, applied to a transport equation in 2D domain, based on a second-order finite volume discretization.