Moving finite element modelling of compressible flow
Applied Numerical Mathematics - Special issue on numerical methods for the Euler equation
The design and analysis of spatial data structures
The design and analysis of spatial data structures
ACM Transactions on Mathematical Software (TOMS)
Adaptive refinement for arbitrary finite-element spaces with hierarchical bases
Journal of Computational and Applied Mathematics
Local modification of meshes for adaptive and/or multigrid finite-element methods
Journal of Computational and Applied Mathematics
Three-dimensional adaptive mesh refinement for hyperbolic conservation laws
SIAM Journal on Scientific Computing
Stability and error estimation for component adaptive grid methods
Applied Numerical Mathematics - Special issue on adaptive mesh refinement methods for CFD applications
Design and Application of a Gradient-Weighted Moving Finite Element Code I: in One Dimension
SIAM Journal on Scientific Computing
Design and Application of a Gradient-Weighted Moving Finite Element Code II: in Two Dimensions
SIAM Journal on Scientific Computing
Fully threaded tree algorithms for adaptive refinement fluid dynamics simulations
Journal of Computational Physics
Algorithms + Data Structures = Programs
Algorithms + Data Structures = Programs
Autonomous Leaves Graph Applied to the Boundary Layer Problem
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
Finite-Element Non-conforming h-Adaptive Strategy Based on Autonomous Leaves Graph
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
An adaptive mesh algorithm for the numerical solution of electrical models of the heart
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
A parallel accelerated adaptive mesh algorithm for the solution of electrical models of the heart
International Journal of High Performance Systems Architecture
Hi-index | 7.30 |
A graph-based implementation of quadtree meshes for dealing with adaptive mesh refinement (AMR) in the numerical solution of evolutionary partial differential equations is discussed using finite volume methods. The technique displays a plug-in feature that allows replacement of a group of cells in any region of interest for another one with arbitrary refinement, and with only local changes occurring in the data structure. The data structure is also specially designed to minimize the number of operations needed in the AMR. Implementation of the new scheme allows flexibility in the levels of refinement of adjacent regions. Moreover, storage requirements and computational cost compare competitively with mesh refinement schemes based on hierarchical trees. Low storage is achieved for only the children nodes are stored when a refinement takes place. These nodes become part of a graph structure, thus motivating the denomination autonomous leaves graph (ALG) for the new scheme. Neighbors can then be reached without accessing their parent nodes. Additionally, linear-system solvers based on the minimization of functionals can be easily employed. ALG was not conceived with any particular problem or geometry in mind and can thus be applied to the study of several phenomena. Some test problems are used to illustrate the effectiveness of the technique.