A path-level exact parallelization strategy for sequential simulation

Sequential Simulation is a well known method in geostatistical modelling. Following the Bayesian approach for simulation of conditionally dependent random events, Sequential Indicator Simulation (SIS) method draws simulated values for K categories (categorical case) or classes defined by K different thresholds (continuous case). Similarly, Sequential Gaussian Simulation (SGS) method draws simulated values from a multivariate Gaussian field. In this work, a path-level approach to parallelize SIS and SGS methods is presented. A first stage of re-arrangement of the simulation path is performed, followed by a second stage of parallel simulation for non-conflicting nodes. A key advantage of the proposed parallelization method is to generate identical realizations as with the original non-parallelized methods. Case studies are presented using two sequential simulation codes from GSLIB: SISIM and SGSIM. Execution time and speedup results are shown for large-scale domains, with many categories and maximum kriging neighbours in each case, achieving high speedup results in the best scenarios using 16 threads of execution in a single machine.Peer ReviewedPostprint (author's final draft

Acceleration strategies for large-scale sequential simulations using parallel neighbour search: Non-LVA and LVA scenarios

This paper describes the application of acceleration techniques into existing implementations of Sequential Gaussian Simulation and Sequential Indicator Simulation. These implementations might incorporate Locally Varying Anisotropy (LVA) to capture non-linear features of the underlying physical phenomena. The imple- mentation focuses on a novel parallel neighbour search algorithm, which can be used on both non-LVA and LVA codes. Additionally, parallel shortest path executions and optimized linear algebra libraries are applied with focus on LVA codes. Execution time, speedup and accuracy results are presented. Non-LVA codes are benchmarked using two scenarios with approximately 50 million domain points each. Speedup results of 2× and 4× were obtained on SGS and SISIM respectively, where each scenario is compared against a baseline code published in Peredo et al. (2018). The aggregated contribution to speedup of both works results in 12× and 50× respectively. LVA codes are benchmarked using two scenarios with approximately 1.7 million domain points each. Speedup results of 56× and 1822× were obtained on SGS and SISIM respectively, where each scenario is compared against the original baseline sequential codes.The authors acknowledge the donated resources from project PID2019-107255GB of the Spanish Ministerio de Economía y Competitividad, and project 2017-SGR-1414 from the Generalitat de Catalunya, Spain.Peer ReviewedPostprint (published version

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

The Iray Light Transport Simulation and Rendering System

While ray tracing has become increasingly common and path tracing is well understood by now, a major challenge lies in crafting an easy-to-use and efficient system implementing these technologies. Following a purely physically-based paradigm while still allowing for artistic workflows, the Iray light transport simulation and rendering system allows for rendering complex scenes by the push of a button and thus makes accurate light transport simulation widely available. In this document we discuss the challenges and implementation choices that follow from our primary design decisions, demonstrating that such a rendering system can be made a practical, scalable, and efficient real-world application that has been adopted by various companies across many fields and is in use by many industry professionals today

Parallelizing RRT on large-scale distributed-memory architectures

This paper addresses the problem of parallelizing the Rapidly-exploring Random Tree (RRT) algorithm on large-scale distributed-memory architectures, using the Message Passing Interface. We compare three parallel versions of RRT based on classical parallelization schemes. We evaluate them on different motion planning problems and analyze the various factors influencing their performance