Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. The algorithms can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms are controlled-error approximations of kinetic Monte Carlo algorithms, departing from the predominant paradigm of creating parallel KMC algorithms with exactly the same master equation as the serial one. Our methodology relies on a spatial decomposition of the Markov operator underlying the KMC algorithm into a hierarchy of operators corresponding to the processors' structure in the parallel architecture. Based on this operator decomposition, we formulate Fractional Step Approximation schemes by employing the Trotter Theorem and its random variants; these schemes, (a) determine the communication schedule} between processors, and (b) are run independently on each processor through a serial KMC simulation, called a kernel, on each fractional step time-window. Furthermore, the proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules.Comment: 34 pages, 9 figure

Cost-Based Optimization of Integration Flows

Integration flows are increasingly used to specify and execute data-intensive integration tasks between heterogeneous systems and applications. There are many different application areas such as real-time ETL and data synchronization between operational systems. For the reasons of an increasing amount of data, highly distributed IT infrastructures, and high requirements for data consistency and up-to-dateness of query results, many instances of integration flows are executed over time. Due to this high load and blocking synchronous source systems, the performance of the central integration platform is crucial for an IT infrastructure. To tackle these high performance requirements, we introduce the concept of cost-based optimization of imperative integration flows that relies on incremental statistics maintenance and inter-instance plan re-optimization. As a foundation, we introduce the concept of periodical re-optimization including novel cost-based optimization techniques that are tailor-made for integration flows. Furthermore, we refine the periodical re-optimization to on-demand re-optimization in order to overcome the problems of many unnecessary re-optimization steps and adaptation delays, where we miss optimization opportunities. This approach ensures low optimization overhead and fast workload adaptation