exascale; parallelization in time; multi-grid; domain decomposition; energy effiency; H matrices
Kreienbuehl A., Benedusi P., Ruprecht D., Krause R. (2017), Time--parallel Gravitational Collapse Simulation, in Communications in Applied Mathematics and Computational Science
, 12(1), 109-128.
Benedusi P., Hupp D., Arbenz P., Krause R. (2016), A Parallel Multigrid Solver for Time--periodic Incompressible Navier--Stokes Equations in 3D, in Numerical Mathematics and Advanced Applications ENUMATH 2015
, Ankara265-273, Springer International Publishing, Berlin265-273.
Grasedyck L., Löbbert C., Wittum G., Nägel A., Schulz V., Siebenborn M., Krause R., Benedusi P., Küster Uwe, Dick Björn (2016), Space and Time Parallel Multigrid for Optimization and Uncertainty Quantification in PDE Simulations, in Neumann Philipp, Bungartz Hans-Joachim, Nagel Wolfgang E. (ed.), Springer, Cham, 507-523.
Today, exascale computers are characterized by billion-way parallelism. Computing on such extreme scale needs methods which scale perfectly and have optimal complexity. This project proposal brings together several crucial aspects of extreme scale solving. First, the solver itself must be of optimal numerical complexity - a requirement becoming more an more severe with increasing problem size - and at the same time scale efficiently on extreme scales of parallelism. Second, simulations on exascale systems will consume a lot of electric power, requiring algorithms and implementations with low power consumption. To that end, the present project combines domain decomposition, parallel multigrid and H-matrices. This technique has the potential to gain top efficiency on extreme scales while still maintaining optimal complexity. To further improve parallelism, this approach is combined with special methods for parallelization in time and solvers for optimization problems. Both cases have additional parallelization potential. Algorithms and implementations will be evaluated for energy efficiency in problem solving. Criteria and models for energy efficiency of numerical solvers will be developed in the project. The team has long standing experience in developing algorithms and software for large scale HPC cooperatively.