Scheduling Massively Parallel Multigrid for Multilevel Monte Carlo Methods

The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly when they are combined with a fast multigrid solver, but to exploit them fully in a parallel environment, sophisticated scheduling strategies are needed. We optimize the concurrent execution across the three layers of the MLMC method: parallelization across levels, across samples, and across the spatial grid. In a series of numerical tests, the influence on the overall performance of the “scalability window” of the multigrid solver (i.e., the range of processor numbers over which good parallel efficiency can be maintained) is illustrated. Different homogeneous and heterogeneous scheduling strategies are proposed and discussed. Finally, large 3D scaling experiments are carried out, including adaptivity

Calibrated cycles and T-duality

For Hitchin's generalised geometries we introduce and analyse the concept of a structured submanifold which encapsulates the classical notion of a calibrated submanifold. Under a suitable integrability condition on the ambient geometry, these generalised calibrated cycles minimise a functional occurring as D-brane energy in type II string theories, involving both so-called NS-NS- and R-R-fields. Further, we investigate the behaviour of calibrated cycles under T-duality and construct non-trivial examples.Comment: 43 pages. v4: formalism and T-duality part considerably expande

Massively Parallel Large Scale Stokes Flow Simulation

In many applications, physical models consisting of a Stokes-type equation that is coupled to a convection-dominated transport equation play an important role, e.g., in mantle-convection or ice-sheet dynamics. In the iterative treatment of such problems the computational cost is usually dominated by the solution procedure for the Stokes part. Hence, we focus on massively scalable and fast multigrid solvers for the arising saddle point problem. To gain deeper insight into the performance characteristics, we evaluate the multigrid efficiency systematically and address the methodology of algorithmic resilience. Three methods based on the HHG software framework will be presented and are shown to solve FE systems with half a billion unknowns even on standard workstations. On petascale systems they furthermore exhibit excellent scalability.This together with the optimised performance on each node leads to superior supercomputing efficiency. Indefinite systems with up to ten trillion (10^13) unknowns can be solved in less than13 minutes compute time

Intranasale Schutzimpfung gegen die Pasteurellose der Kaelber: Klinische Pruefung und Antikoerpernachweis im Nasenschleim mit dem ELISA

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