Mixed Precision Methods
Variable Length Integer Encoding+
The IEEE 754 floating point standard is ubiquitous, however, it is rather inflexible due to a fixed-length exponent encoding and some additional drawbacks. Multiple new format families with variable length encoding of the exponent (tapered accuracy) have been suggested. But there are so many more possibilities, how do we know what is best? We develop a framework which allows the exploration of all options in variable-length integer encoding, i.e. all uniquely decipherable exhaustive binary codes can be represented.
Mixed-Precision Methods+
★Double accuracy with single precision GPUs and FPGAs★ To obtain a result of high accuracy it is not necessary to compute all intermediate results with high precision. Mixed precision methods apply high precision computations only where necessary and save space or time without decreasing the accuracy of the final solution.
Balanced Geometric Multigrid+
Neither solvers with best numerical convergence nor solvers with best parallel efficiency are the best choice for the fast solution of PDE problems in practice. The fastest solvers require a delicate balance between their numerical and hardware characteristics. Balancing both aspects we can even parallelize completely sequential preconditioners with large parallel speedup and hardly any loss in numerical performance.
GPU-Cluster Computing
★Minimally invasive acceleration of legacy code on GPU-clusters★ A single GPU already offers two levels of parallelism, but similar to CPUs, demand for higher performance and larger problem sizes leads to the utilization of GPU-clusters, in which every cluster node is equipped with GPUs. This adds the intra-node and inter-node parallelism. The main challenge for these heterogeneous systems is the enormous discrepancy in the bandwidth between the two finer and two coarser levels of parallelism and their integration in legacy code.