Adaptive refinement for arbitrary finite-element spaces with hierarchical bases
Journal of Computational and Applied Mathematics
Proceedings of international centre for mathematical sciences on Grid adaptation in computational PDES : theory and applications: theory and applications
Discontinuous Galerkin Spectral/hp Element Modelling of Dispersive Shallow Water Systems
Journal of Scientific Computing
Journal of Computational Physics
A refinement-tree based partitioning method for dynamic load balancing with adaptively refined grids
Journal of Parallel and Distributed Computing
A Cache-Aware Algorithm for PDEs on Hierarchical Data Structures Based on Space-Filling Curves
SIAM Journal on Scientific Computing
Optimization of sparse matrix-vector multiplication on emerging multicore platforms
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
International Journal of Computational Science and Engineering
Numerical Simulation of Particle Transport in a Drift Ratchet
SIAM Journal on Scientific Computing
Efficient storage and processing of adaptive triangular grids using sierpinski curves
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
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We present an approach to the numerical simulation of dynamically adaptive problems on recursively structured adaptive triangular grids. The intended application is the simulation of oceanic wave propagation (e.g., tsunami simulation) based on the shallow water equations. For the required 2D dynamically adaptive discretization, we adopt a grid generation process based on recursive bisection of triangles along marked edges. The recursive grid generation may be described via a respective refinement tree, which is sequentialized according to a Sierpinski space-filling curve. This allows a storage scheme for the adaptive grid that requires only a minimal amount of memory. Moreover, the sequentialization and, hence, the locality properties induced by the space-filling curve are retained throughout adaptive refinement and coarsening of the grid. Conforming adaptive refinement and coarsening, as well as time-stepping techniques for time-dependent systems of partial differential equations, are implemented using an inherently cache-efficient processing scheme, which is based on the use of stacks and stream-like data structures and a traversal of the adaptively refined grid along the Sierpinski curve. We demonstrate the computational efficiency of the approach on the solution of a simplified version of the shallow water equations, for which we use a discontinuous Galerkin discretization. Special attention is paid to the memory efficiency of the implementation.