AuthorsKöppl, Tobias Weinzierl & Tobias
KAUST Grant NumberUKc0020
Permanent link to this recordhttp://hdl.handle.net/10754/665995
MetadataShow full item record
AbstractWe study the time-dependent heat equation on its space-time domain that is discretised by a k-spacetree. k-spacetrees are a generalisation of the octree concept and are a discretisation paradigm yielding a multiscale representation of dynamically adaptive Cartesian grids with low memory footprint. The paper presents a full approximation storage geometric multigrid implementation for this setting that combines the smoothing properties of multigrid for the equation's elliptic operator with a multiscale solution propagation in time. While the runtime and memory overhead for tackling the all-in-one space-time problem is bounded, the holistic approach promises to exhibit a better parallel scalability than classical time stepping, adaptive dynamic refinement in space and time fall naturally into place, as well as the treatment of periodic boundary conditions of steady cycle systems, on-time computational steering is eased as the algorithm delivers guesses for the solution's long-term behaviour immediately, and, finally, backward problems arising from the adjoint equation benefit from the the solution being available for any point in space and time. © 2012 Global-Science Press.
CitationKöppl, T. W. & T. (2012). A Geometric Space-Time Multigrid Algorithm for the Heat Equation. Numerical Mathematics: Theory, Methods and Applications, 5(1), 110–130. doi:10.4208/nmtma.m12si07
SponsorsThis publication is partially based on work supported by Award No. UKc0020, made by the King Abdullah University of Science and Technology (KAUST).
PublisherGlobal Science Press