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One of the main constraints to the operational use of Integrated Surface and Subsurface Hydrologic Modelling (ISSHM) is the computational cost of such a complex approach. The growth of High-Performance Computing (HPC) has continuously pushed forward this limit, targeting the objective of "hyper-resolution" modelling. The Extended Cellular Automata (XCA) paradigm allows easy parallelization of numerical code and can be used in different HPC systems. Moreover, XCA have other unique features, like asynchronism, that can further break down the elapsed time.HydroCAL is an integrated surface-subsurface Cellular Automata Layer hydrological model built by coupling a diffusive-like 2D water surface routing module and a 3D subsurface routing module based on the variably saturated Richards' equation. The model was implemented by adopting the parallel scientific software library Open Computing Abstraction Layer (OpenCAL), which allows researchers to exploit different parallelization techniques, hardware architectures and XCA-specific features.Here we extend the HydroCAL model's capabilities, including groundwater and evapotranspiration modules that significantly contribute to the baseflow generation and river reach activation/deactivation dynamics, allowing continuous simulations beyond the storm-event scale. The enhanced model is used at ultra-high resolution (100 m) in a small steep-orography headwater Mediterranean catchment characterized by high hydrogeological heterogeneity. A multivariate calibration and validation approach is adopted over long-term simulations, using the observed active stream network dynamics and the recorded streamflow at the catchment outlet.The results show that HydroCAL can adequately reproduce the hydrological response, simulating several multipeak events and reproducing the recession phases. Moreover, groundwater behaviour contributes to the simulation of the complex river network activation and deactivation dynamics. Overall, the HydroCAL model implementation upon the XCA paradigm allows highly detailed coupled simulations for long periods with reasonable computational times.

The allocation of the computational load across different processing elements is an important issue in parallel computing. Indeed, an unbalanced load distribution can strongly affect the performances of a parallel system caused by an excess of synchronization idle times due to less loaded processes waiting for more loaded ones. In this article, we focus on the load balancing issues in the context of the parallel execution of spatial-related applications where the domain space is partitioned in regions that are assigned to different processing elements. In particular, without loss of generality, we consider the well-known spatial-related Cellular Automata computational paradigm for evaluating the proposed dynamic load balancing approach. The main contribution of this article is the derivation of simple closed-form expressions that allow to compute the optimal workload assignment in a dynamic fashion, with the goal of guaranteeing a fully balanced workload distribution during the parallel execution. Based on these expressions, an algorithm for balanced execution of cellular automata is presented and implemented using the MPI technology. Eventually, an experimental section practically shows the behaviour of the proposed dynamic load balancing approach and proves its performance improvement, compared to the not-balanced version, as witnessed by the appreciable reduction of execution times.

OpenCAL is a scientific software library specifically developed for the simulation of 2D and 3D complex dynamical systems on parallel computational devices. It is written in C/C++ and relies on OpenMP/OpenCL and MPI for parallel execution on multi-/many-core devices and clusters of computers, respectively. The library provides the Extended Cellular Automata paradigm as a high-level formalism for modeling complex systems on structured computational grids. As a consequence, it can be used as a parallel explicit solver of ordinary and partial differential equations through classical methods, including finite-difference and finite-volume. Here the latest version of the library is described, introducing the MPI infrastructure over the 3D OpenCL and 2D/3D OpenMP components. The implementation of a three-dimensional unsaturated flow model based on a direct discrete formulation of the Richards’ equation is also shown, corresponding to a finite-difference scheme. Computational performances have been assessed on both a scientific workstation equipped with a dual Intel Xeon socket and three Nvidia GPUs, and a 16 nodes cluster with a fast interconnection network. The OpenCAL embedded quantization optimization is also discussed and exploited to drastically reduce computing time.

The Integrated Surface and Subsurface Hydrologic Modeling (ISSHM) approach, based on the coupling of physical-based surface and subsurface routing processes, evolved significantly in the last decades, also thanks to the continuously increasing capabilities offered by high-performance computing (HPC). The Extended Cellular Automata (XCA) paradigm perfectly fits the needs of HPC infrastructures, due to its inherent aptitude for parallel computing and other specific features like asynchronism that allow not only parallelization but also the reduction of the computational cost.We present HydroCAL, a new ISSHM based on the Extended Cellular Automata paradigm linking a two-dimensional weighted XCA surface routing model with a three-dimensional XCA subsurface model. The model was implemented in the parallel software library Open Computing Abstraction Layer (OpenCAL), which allows users to exploit several parallelization strategies, hardware architectures and XCA features.Preliminarily, the subsurface model was tested in several thousand synthetical test cases to assess the effects produced by an asynchronous functionality based on a fixed threshold rule on the hydraulic head difference. The results show the high efficiency of the asynchronous XCA model in terms of elapsed time, preserving the accuracy of the results.Then, the coupled surface and subsurface HydroCAL modules were tested with high-resolution (101 m) simulations in a small headwater Mediterranean catchment characterized by high hydrogeological heterogeneity. The model parameters were calibrated and validated using different events, characterized by several discharge peaks, during two years.The results show that the model can accurately catch the hydrological response, reproducing multi-peak events with correct peak times and discharge values, simulating adequately also the recession phases. At the same time, the XCA model implementation permits highly detailed coupled simulations with computational times adequate to operational (even real-time) purposes.Further study will regard the application of different asynchronism rules on both the surface and subsurface modules and the addition of other modules concerning subsurface-groundwater and land surface-atmosphere interaction.

Here we present a first multi-node/multi-GPU implementation of OpenCAL for grid-based high-performance numerical simulation. OpenCL and MPI have been adopted as low-level APIs for maximum portability and performance evaluated with respect to three different benchmarks, namely a Sobel edge detection filter, a Julia fractal generator, and the SciddicaT Cellular Automata model for fluid-flows simulation. Different hardware configurations of a dual-node test cluster have been considered, allowing for executions up to four GPUs. Optimal performance has been achieved in consideration of the compute/memory bound nature of both benchmarks and hardware configurations.

Modelling subsurface flow processes is one of the key factors to describe the water cycle. To this aim, a variably saturated flow model was developed based on the Extended Cellular Automata (XCA) formalism and used to simulate an ensemble of 100 synthetic two-dimensional plots with heterogeneous hydraulic properties. The model was implemented exploiting the functionalities of the OpenCAL library, which allowed high computational efficiency using multi-core (CPU) processors and even higher performances with many-core (GPGPU) architectures.

Extended Cellular Automata (XCA) represent one of the most known parallel computational paradigm for the modeling and simulation of complex systems on stenciled structured grids. However, the formalism does not perfectly lend itself to the modeling of multiple automata were two or more models co-evolve by interchanging information and by synchronizing during the dynamic evolution of the system. Here we propose the Extended Cellular Automata Network (XCAN) formalism, an extension of the original XCA paradigm in which different automata are described by means of a graph, with vertices representing automata and inter-relations modeled by a set of edges. The formalism is applied to the modeling of a theoretical 2D/3D coupled system, where space/time variance and synchronization aspects are pointed out.

A computationally efficient surface to groundwater coupled hydrological model is being developed based on the Extended Cellular Automata (XCA) formalism. The three-dimensional unsaturated flow model was the first to be designed and implemented in OpenCAL. Here, the response of the model with respect to small variations of the quantization threshold has been assessed, which is the OpenCAL’s quantization algorithm’s parameter used for evaluating cell’s steady state condition. An unsaturated flow test case was considered where the elapsed times of both the non quantized execution and the execution run by setting the quantization threshold to zero (with respect to the moist content variable) were already evaluated. The model response has been assessed in terms of both accuracy and computational performance in the case of an MPI/OpenMP hybrid execution. Results have pointed out that a very good tradeoff between accuracy and computational performance can be achieved, allowing for a considerable speed-up of the model against a very limited loss of precision.

Cellular Automata (CA) are parallel models well-suited for studying complex systems that are based on local rules of evolution. Notable examples of application are found in fluid-dynamics, crowd simulation, flow-simulation and many more. Nevertheless, CA can be fruitfully exploited as a support in numerical approaches, such as finite element and finite volume methods. Though easily parallelizable by domain partitioning among the nodes of a parallel system, the performance and scalability of cellular automata executed on parallel/distributed machines are limited due to the need of synchronizing nodes at each computational step. With the aim of reducing the synchronization burden, we here present a preliminary study on techniques stemmed from the Discrete-Event Simulation field for the optimization of CA on distributed memory architectures. Preliminary results, executed in a distributed memory environment, have shown the usefulness of the considered approach in reducing execution times and therefore in improving the speed up of the parallel execution of the test case.

Partitioning computational load over different processing elements is a crucial issue in parallel computing. This is particularly relevant in the case of parallel execution of structured grid computational models, such as Cellular Automata (CA), where the domain space is partitioned in regions assigned to the parallel computing nodes. In this work, we present a dynamic load balancing technique that provides for performance improvements in structured grid model execution on distributed memory architectures. First tests implemented using the MPI technology have shown the goodness of the proposed technique in sensibly reducing execution times with respect to not-balanced parallel versions.

This article introduces OpenCAL, a new open source computing abstraction layer for multi- and many-core computing based on the Extended Cellular Automata general formalism. OpenCAL greatly simplifies the implementation of structured grid applications, contextually making parallelism transparent to the user. Different OpenMP- and OpenCL-based implementations have been developed, together with a preliminary MPI-based distributed memory version, which is currently under development. The system software architecture is presented and underlying data structures and algorithms described. Numerical correctness and efficiency have been assessed by considering the S c i d d i c a T Computational Fluid Dynamics landslide simulation model as reference example. Eventually, a comprehensive study has been performed to devise the best platform for execution as a function of numerical complexity and computational domain extent. Results obtained have highlighted the OpenCAL’s potential for numerical models development and their execution on the most suitable high-performance parallel computational device.

Cellular Automata (CA) are particularly suitable for physically-based modelling of complex hydrological processes due to their inherent aptitude for parallel computing. Nevertheless, other CA specific features like asynchronism could be exploited to enhance further the computational efficiency. This note introduces an innovative activation/deactivation rule enabling for the first time the practical application of asynchronous CA to subsurface flow problems. The asynchronism rule, consisting of a threshold depending on the spatial total hydraulic head difference between each automaton and its neighbourhood, was implemented in the new OpenCAL parallel software library using the Extended CA (XCA) paradigm. It was tested performing hundreds of wet front propagation simulations in a comprehensive probabilistic framework, considering several thresholds and addressing both two- and three-dimensional domains with heterogeneous hydraulic properties. Furthermore, realistic simulations of a drip-irrigated field entailing combined infiltration/exfiltration cycles were carried out. The application of the asynchronism rule generated considerable computational benefits for all the test cases, even adopting low threshold values, reducing the elapsed time by up to 80-85% while preserving numerical accuracy. In particular, the three-dimensional simulation of the drip-irrigated field demonstrated the practical relevance of the approach. The computational improvement produced by the combined effect of parallel computing and the proposed asynchronism strategy enables increased space-time resolution on wider study areas and further developments focusing on the simulation of computationally demanding relevant processes.

The Cellular Automata paradigm is an efficient tool to model and study complex systems such as traffic simulation, lava flows and swarm based behaviour. In addition, cellular automata can be profitably used in many mathematical problems such as differential equations and chaos theory. Due to their inherent parallel nature, cellular automata can be efficiently parallelized among a set of computing nodes in order to scale and speed up their execution. This paper presents a preliminary study on different parallelizzation techniques for structured grid models such as cellular automata on distributed memory architectures. In particular, three strategies are presented and compared in order to evaluate their efficiency in terms of speed-up. An experimental section shows the performance achieved by the three strategies when a real-life application, namely the SciddicaT cellular automata model for debris-flows simulation, is adopted.

A fully-coupled from surface to groundwater hydrological model is being developed based on the Extended Cellular Automata formalism (XCA), which proves to be very suitable for high performance computing. In this paper, a preliminary module related to three-dimensional saturated flow in porous media is presented and implemented by using the OpenCAL parallel software library. This allows to exploit distributed systems with heterogeneous computational devices. The proposed model is evaluated in terms of both accuracy and precision of modeling results and computational performance, using single layered three-dimensional test cases at different resolutions (from local to regional scale), simulating pumping from one or more wells, river-groundwater interactions and varying soil hydraulic properties. Model accuracy is compared with analytic, when available, or numerical (MODFLOW 2005) solution, while the computational performance is evaluated using an Intel Xeon CPU socket. Overall, the XCA-based model proves to be accurate and, mainly, computationally very efficient thanks to the many options and tools available with the OpenCAL library.

Computational structured grids are often adopted in the simulation of complex systems, since they offer a good trade off between accuracy and efficiency [1]. Different formal models have been proposed in Literature to describe the computational process on the grid, such as Extended Cellular Automata [1] and Cellular Automata Neworks [3]. Here we propose a new formalism called Structure+ with the aim of modeling multidimensional space-time discrete complex systems by means of one or more structured grids, each one with its own dimensionality and dimension. Both local and global transition rules can be defined to permit the different grids to evolve. Interface operators, like aggregation and disaggregation functions, can also be defined to allow the different domains to communicate and synchronize. A first example of a coupled surface to groundwater hydrological model is presented. Considerations about parallel computational aspects are eventually discussed.

Here we present different preliminary parallel grid-based implementations of a simple particle system with the purpose to evaluate its performances on multi- and many-core computational devices. The system is modeled by means of the Discrete Element Method and the Extended Cellular Automata formalism, while OpenMP and OpenCL are used for parallelization. In particular, both the 3.1 and 4.5 OpenMP specifications have been considered, the latter also able to run on many-core computational devices like GPUs. The results of a first test simulation performed by considering a cubic domain with about 316,000 particles have shown a clear advantage of OpenCL on the considered Tesla K40 Nvidia GPU, while the OpenMP 3.1 implementation has performed better than the corresponding OpenMP 4.5 on the considered Intel Xeon E5-2650 16-thread CPU.

We here present computational results as performed by the new OpenCAL scientific library for seamless implementation of models referred to Computational Fluid Dynamics (CFD). In particular, OpenCAL allows for the straightforward definition of Cellular Automata- and Finite Differences-based simulation models of complex systems, by also supporting Extended Cellular Automata and all those computing paradigms based on regular computational grids. Two different parallel implementations are presented, which permit to exploit both multi-core CPUs on shared memory computers, and a wide range of heterogeneous devices like GPUs and other many-core coprocessors. Experiments, referred to a well-known cellular automata, namely the SCIDDICA S 3−hex model for landslide simulation, exhibit good scalability, and numerical correctness and efficiency have been assessed on both multi-core CPUs and different many-core coprocessors. The good performances that were achieved in all benchmarks confirm the library's suitability for model development of complex systems and their execution on parallel heterogeneous computational devices.

The performance and scalability of cellular automata, when executed on parallel/distributed machines, are limited by the necessity of synchronizing all the nodes at each time step, i.e., a node can execute its code only after all the other nodes have executed the previous step. However, if the code is parallelized by partitioning the space of the automata, these synchronization requirements can be relaxed: indeed, a node that manages a given portion of the cellular automata can execute a new step after synchronizing only with the nodes that manage the adjacent portions, while the remaining nodes can execute different time steps. This can be a notable advantage in many novel and increasingly popular applications of cellular automata, such as smart city applications, simulation of natural phenomena, etc., in which the execution times can be different and variable, due to the heterogeneity of machines and/or of the data and/or of the different functions. Indeed, a longer execution time at a node does not slow down the execution at all the other nodes but only at the neighboring nodes. This is particularly advantageous when the nodes that act as a bottleneck can vary during the execution. The goal of the paper is to analyze the benefits that can be achieved with the described approach when different space partitioning strategies are taken into account: i.e., the mono-and the two-dimensional partitioning. Experiments referred to a well-known cellular automata, namely the SciddicaS3-hex model for landslide simulation, exhibit good scalability and prove that the partitioning scheme adopted can result crucial for improving the overall computational performances.

Particle tracking plays an important role in numerous fields of science. In this paper, we present TraCCA, an algorithm for detecting and tracking particles based on geometrical difference evaluation and centroid displacement analysis to reconstruct the trajectories. This method works for n-dimensional input data provided that particles are represented by at least a centroid space coordinate and a geometrical entity which describe their shape. Since 2-D images are a common source of such data, we also present a framework for image-manipulation based on Extended Cellular Automata (XCA). We have applied and validated TraCCA in investigating the motility of B. subtilis. injected in a microfluidic device using 4100 images taken at 100 frames per second. Results show that the framework is able to reconstruct the trajectories as computed motion parameters are in accordance with the ones reported in the literature.

This work presents an effective implementation of a numerical model for complete eco-hydrological Cellular Automata modeling on Graphical Processing Units (GPU) with OpenCL (Open Computing Language) for heterogeneous computation (i.e., on CPUs and/or GPUs). Different types of parallel implementations were carried out (e.g., use of fast local memory, loop unrolling, etc), showing increasing performance improvements in terms of speedup, adopting also some original optimizations strategies. Moreover, numerical analysis of results (i.e., comparison of CPU and GPU outcomes in terms of rounding errors) have proven to be satisfactory. Experiments were carried out on a workstation with two CPUs (Intel Xeon E5440 at 2.83GHz), one GPU AMD R9 280X and one GPU nVIDIA Tesla K20c. Results have been extremely positive, but further testing should be performed to assess the functionality of the adopted strategies on other complete models and their ability to fruitfully exploit parallel systems resources.

GPGPU (General Purpose computing on Graphics Processing Units) has marked a revolution in the field of Parallel Computing allowing to achieve computational performance unimaginable until a few years ago. This hardware has proven to be extremely reliable and suitable to simulate Cellular Automata (CA) models for modeling complex systems whose evolution can be described in terms of local interactions. Starting from previous GPGPU implementations of CA models with CUDA, this paper presents an effective implementation of a well-known numerical model for simulating lava flows on Graphical Processing Units (GPU) based on the OpenCL (Open Computing Language) standard. In addition, a preliminary Civil Defence application related Hazard maps of an area located at Mt. Etna volcano (South Italy), confirms the validity of OpenCL and both low-cost and high-end graphics hardware as an alternative to expensive solutions for the simulation of CA models.