Programming the Intel 80386
Computing
High-order accurate discontinuous finite element solution of the 2D Euler equations
Journal of Computational Physics
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The C++ standard library: a tutorial and reference
The C++ standard library: a tutorial and reference
Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves
Parallel Computing - Special issue on parallelization techniques for numerical modelling
Navigating through triangle meshes implemented as linear quadtrees
ACM Transactions on Graphics (TOG)
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Switching and Finite Automata Theory: Computer Science Series
Switching and Finite Automata Theory: Computer Science Series
Introduction to Algorithms
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Constant-Time Neighbor Finding in Hierarchical Tetrahedral Meshes
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Rendering and managing spherical data with sphere quadtrees
VIS '90 Proceedings of the 1st conference on Visualization '90
A Multilevel Preconditioner for the Interior Penalty Discontinuous Galerkin Method
SIAM Journal on Numerical Analysis
The Art of Computer Programming, Volume 4, Fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams
Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers
Hi-index | 0.00 |
Adaptive multiscale methods are among the many effective techniques for the numerical solution of partial differential equations. Efficient grid management is an important task in these solvers. In this paper we focus on this problem for discontinuous Galerkin discretization methods in 2 and 3 spatial dimensions and present a data structure for handling adaptive grids of different cell types in a unified approach. Instead of tree-based techniques where connectivity is stored via pointers, we associate each cell that arises in the refinement hierarchy with a cell identifier and construct algorithms that establish hierarchical and spatial connectivity. By means of bitwise operations, the complexity of the connectivity algorithms can be bounded independent of the level. The grid is represented by a hash table which results in a low-memory data structure and ensures fast access to cell data. The spatial connectivity algorithm also supports the application of quadrature rules for face integrals that occur in discontinuous Galerkin discretizations. The concept allows us to implement discontinuous Galerkin methods largely independent of spatial dimension and cell type. We demonstrate this by outlining how typical algorithmic tasks that arise in these implementations can be performed with our data structure. In computational tests we compare our approach with that of a classical implementation using pointers.