Simulation Speedup Research Articles

A Novel Linking-Domain Extraction Decomposition Method for Parallel Electromagnetic Transient Simulation of Large-Scale AC/DC Networks

Domain decomposition of the network conductance matrix is one of the efficient approaches to solve large-scale networks in parallel, wherein the most commonly-used non-iterative method is the Schur complement (SC) method. However, the SC method could not obtain the network conductance matrix inversion directly, and the computational cost will increase fast when the overlapping domain expands. In this work, a novel Linking-Domain Extraction (LDE) based decomposition method is proposed, in which the network matrix is expressed as the sum of a linking-domain matrix (LDM) and a diagonal block matrix (DBM) composed of multiple block matrices in diagonal. Through mathematical analysis over LDM, one lemma about the nature of LDM and its proof are proposed. Based on this lemma, the general formulation of the inverse matrix of the sum of LDM and DBM can be found using the Woodbury matrix identity, and based on the formulation the network matrix inversion can be directly computed in parallel to significantly accelerate the matrix inversion process. Test systems were implemented on both the FPGA and GPU parallel architectures, and the simulation results and speed-ups over the SC method and Gauss-Jordan elimination demonstrate the validity and efficiency of the proposed LDE method.

Impact of the Partitioning Method on Multidimensional Adaptive-Chemistry Simulations

The large number of species included in the detailed kinetic mechanisms represents a serious challenge for numerical simulations of reactive flows, as it can lead to large CPU times, even for relatively simple systems. One possible solution to mitigate the computational cost of detailed numerical simulations, without sacrificing their accuracy, is to adopt a Sample-Partitioning Adaptive Reduced Chemistry (SPARC) approach. The first step of the aforementioned approach is the thermochemical space partitioning for the generation of locally reduced mechanisms, but this task is often challenging because of the high-dimensionality, as well as the high non-linearity associated to reacting systems. Moreover, the importance of this step in the overall approach is not negligible, as it has effects on the mechanisms’ level of chemical reduction and, consequently, on the accuracy and the computational speed-up of the adaptive simulation. In this work, two different clustering algorithms for the partitioning of the thermochemical space were evaluated by means of an adaptive CFD simulation of a 2D unsteady laminar flame of a nitrogen-diluted methane stream in air. The first one is a hybrid approach based on the coupling between the Self-Organizing Maps with K-Means (SKM), and the second one is the Local Principal Component Analysis (LPCA). Comparable results in terms of mechanism reduction (i.e., the mean number of species in the reduced mechanisms) and simulation accuracy were obtained for both the tested methods, but LPCA showed superior performances in terms of reduced mechanisms uniformity and speed-up of the adaptive simulation. Moreover, the local algorithm showed a lower sensitivity to the training dataset size in terms of the required CPU-time for convergence, thus also being optimal, with respect to SKM, for massive dataset clustering tasks.

Data-driven uncertainty analysis of distribution networks including photovoltaic generation

This paper investigates residential distribution networks with uncertain loads and photovoltaic distributed generation. An original probabilistic modeling of consumer demand and photovoltaic generation is presented that is based on the analysis of large set of data measurements. It is shown how photovoltaic generation is described by complex non-standard distributions that can be described only numerically. Probabilistic analysis is performed using an enhanced version of the Polynomial Chaos technique that exploits a proper set of polynomial basis functions. It is described how such functions can be generated from the numerically available data. Compared to other approximate methods for probabilistic analysis, the novel technique has the advantages of modeling accurately truly nonlinear problems and of directly providing the detailed Probability Density Function of relevant observable quantities affecting the quality of service. Compared to standard Monte Carlo method, the proposed technique introduces a simulation speedup that depends on the number of random parameters. Numerical applications to radial and weakly meshed networks are presented where the method is employed to explore overvoltage, unbalance factor and power loss, as a function of photovoltaic penetration and/or network configuration.

Hardware-Assisted Simulation of Voltage-Behind-Reactance Models of Electric Machines on FPGA

This paper studies the acceleration of numerical simulations executed on Field-Programmable Gate Arrays (FPGAs) for electric machines presented by voltage-behind-reactance (VBR) models. In VBR models, the stator dynamics are modeled in abc coordinates, while the rotor dynamics are formulated in qd reference frame. Both induction motors and synchronous generators, operating without and with magnetic saturation, are considered. Once VBR models of these machine types are reviewed, their dynamic models are discretized using Runge-Kutta numerical routines. The detailed mapping of such discrete models to FPGA is provided using High-Level Synthesis, which directly converts untimed descriptions into VHDL or Verilog. An automated method finds the fastest FPGA architecture by finding the best set of synthesis options. Experimental results show that our FPGA-based acceleration flow leads to about 92-168 times average simulation speed-up for various machine types compared to the MATLAB simulation.

Hydraulic System Modeling with Recurrent Neural Network for the Faster Than Real-Time Simulation

Depending on the task of a decision-support system, the underlying computer simulation can be carried out in real time or faster than real time. The required high simulation speed is a major obstacle in employing the more advanced simulation models. The work addresses the question of the recurrent neural network (RNN) usage for the faster than real-time simulation of hydraulic systems. Mathematical models of such systems are computationally expensive for numerical integration due to their high non-linearity and numerical stiffness. In this paper, a mathematical-based simulation model has been created using an experimentally verified mathematical model of a hydraulic position servo system (HPS). A RNN of the NARX architecture has been developed, trained and tested on the training data produced by the mathematical-based simulation model. A preprocessing technique has been developed and applied to the training data in order to speed-up the training and simulation processes. The obtained results for the first time show that the employment of the RNN together with the developed preprocessing technique ensures the simulation speed-up of the complex hydraulic system at the expense of a small accuracy decrease. In the considered case of the HPS, a simulation speed-up of factor 4.8 has been obtained.

Speedup in classical simulation of Gaussian boson sampling

Gaussian boson sampling is an alternative model for demonstrating quantum computational supremacy, where squeezed states are injected into every input mode, instead of applying single photons as in the case of standard boson sampling. Here by analyzing numerically the computational costs, we establish a lower bound for achieving quantum computational supremacy for a class of Gaussian boson-sampling problems. Specifically, we propose a more efficient method for calculating the transition probabilities, leading to a significant reduction of the simulation costs. Particularly, our numerical results indicate that one can simulate up to 18 photons for Gaussian boson sampling at the output subspace on a normal laptop, 20 photons on a commercial workstation with 256 cores, and about 30 photons for supercomputers. These numbers are significantly smaller than those in standard boson sampling, suggesting that Gaussian boson sampling could be experimentally-friendly for demonstrating quantum computational supremacy.

Multigrid dual-time-stepping lattice Boltzmann method.

The lattice Boltzmann method often involves small numerical time steps due to the acoustic scaling (i.e., scaling between time step and grid size) inherent to the method. In this work, a second-order dual-time-stepping lattice Boltzmann method is proposed in order to avoid any time-step restriction. The implementation of the dual time stepping is based on an external source in the lattice Boltzmann equation, related to the time derivatives of the macroscopic flow quantities. Each time step is treated as a pseudosteady problem. The convergence rate of the steady lattice Boltzmann solver is improved by implementing a multigrid method. The developed solver is based on a two-relaxation time model coupled to an immersed-boundary method. The reliability of the method is demonstrated for steady and unsteady laminar flows past a circular cylinder, either fixed or towed in the computational domain. In the steady-flow case, the multigrid method drastically increases the convergence rate of the lattice Boltzmann method. The dual-time-stepping method is able to accurately reproduce the unsteady flows. The physical time step can be freely adjusted; its effect on the simulation cost is linear, while its impact on the accuracy follows a second-order trend. Two major advantages arise from this feature. (i) Simulation speed-up can be achieved by increasing the time step while conserving a reasonable accuracy. A speed-up of 4 is achieved for the unsteady flow past a fixed cylinder, and higher speed-ups are expected for configurations involving slower flow variations. Significant additional speed-up can also be achieved by accelerating transients. (ii) The choice of the time step allows us to alter the range of simulated timescales. In particular, increasing the time step results in the filtering of undesired pressure waves induced by sharp geometries or rapid temporal variations, without altering the main flow dynamics. These features may be critical to improve the efficiency and range of applicability of the lattice Boltzmann method.

Adaptive Abstraction-Level Conversion Framework for Accelerated Discrete-Event Simulation in Smart Semiconductor Manufacturing

Speeding up the simulation of discrete-event wafer-fabrication models is essential for fast decision-making to handle unexpected events in smart semiconductor manufacturing because decision-parameter optimization requires repeated simulation execution based on the current manufacturing situation. In this paper, we present a runtime abstraction-level conversion approach for discrete-event fab models to gain simulation speedup. During the simulation, if the fab's machine group model reaches a steady state, then the proposed method attempts to substitute this group model with a mean-delay model (MDM) as a high abstraction level model. The MDM abstracts detailed event-driven operations of subcomponents in the group into an average delay based on the queuing modeling, which can guarantee acceptable accuracy in predicting the performance of steady-state queuing systems. To detect the steadiness, the proposed abstraction-level converter (ALC) observes the queuing parameters of low-level groups to identify the statistical convergence of each group's work-in-progress (WIP) level. When a group's WIP level is converged, the output-to-input couplings between the models are revised to change a wafer-lot process flow from the low-level group to a MDM. When the ALC detects lot-arrival changes or any wafer processing status change (e.g., a machine-down), the high-level model is switched back to its corresponding low-level group model. During high-to-low level conversion, the ALC generates dummy wafer-lot events to re-initialize the machine states. The proposed method was applied to various case studies of wafer-fab systems and achieved simulation speedups up to about 4 times with 0.6 to 8.3% accuracy degradations.

Geant4 performance optimization in the ATLAS experiment

Software improvements in the ATLAS Geant4-based simulation are critical to keep up with evolving hardware and increasing luminosity. Geant4 simulation currently accounts for about 50% of CPU consumption in ATLAS and it is expected to remain the leading CPU load during Run 4 (HL-LHC upgrade) with an approximately 25% share in the most optimistic computing model. The ATLAS experiment recently developed two algorithms for optimizing Geant4 performance: Neutron Russian Roulette (NRR) and range cuts for electromagnetic processes. The NRR randomly terminates a fraction of low energy neutrons in the simulation and weights energy deposits of the remaining neutrons to maintain physics performance. Low energy neutrons typically undergo many interactions with the detector material and their path becomes uncorrelated with the point of origin. Therefore, the response of neutrons can be efficiently estimated only with a subset of neutrons. Range cuts for electromagnetic processes exploit a built-in feature of Geant4 and terminate low energy electrons that originate from physics processes including conversions, the photoelectric effect, and Compton scattering. Both algorithms were tuned to maintain physics performance in ATLAS and together they bring about a 20% speed-up of the ATLAS Geant4 simulation. Additional ideas for improvements, currently under investigation, will also be discussed in this paper. Lastly, this paper presents how the ATLAS experiment utilizes software packages such as Intel’s VTune to identify and resolve hot-spots in simulation.

Speed-up of scattered field formulation of FDTD method combining with time-domain EFIE by using spherical harmonic expansion of Green’s function

This paper proposes a scattered field formulation of the finite-difference time domain method (S-FDTD) combining with a time-domain electric field integral equation (TD-EFIE) based on surface equivalence theorem. The scattered field formulation enables us to reduce computation cost effectively for the case that scatterers are located at a far distance from field sources of electromagnetic wave since we need to calculate the scattered field component only on the region in the vicinity of the scatterers. Then it is required for the use of the scattered field formulation that the field source for the incident field component has to be expressed by any analytical solutions such as a point dipole source, plane wave, and so on. In this work, the scattered field formulation of the FDTD method is applied to cases that there are no analytical expressions of the field sources, in which the field source contains conductors such as antennas, combining with the TD-EFIE on a virtual surface which encloses the field sources. Then, it is known that calculation of the TD-EFIE itself is time consuming. This paper considers speed-up of the S-FDTD simulation based on the TD-EFIE using a spherical harmonic expansion of Green’s function of Helmholtz equation, additionally.

Speed-up of simulation of magnetization process for large-scale HTS undulator of X-FEL based on power-law macro-model

The Pure-type HTS undulator is proposed to achieve a high-intensity magnetic field and small size undulator for a compact free-electron laser (FEL). A high precision simulation is required before making the real machine since the sizes and positions are difficult to adjust after the HTSs are magnetized in the cryostat. For this purpose, authors have been developed a numerical simulation code for the magnetization process of HTS undulator of X-FEL based on the power-law macro-model. In this paper, the previously developed simulation code can be speeded up by carefully optimizing the parameters of the power-law macro-model for the 3-HTS magnets model and a large-scale simulation can be performed in an acceptable time by using a multipole expansion for the Biot–Savart law. In addition, for practical applications, the influence of the fluctuation of the magnets thickness and critical current for the electron trajectory are evaluated by using the speed-up simulation code.

Meeting the challenge of JUNO simulation with Opticks: GPU optical photon acceleration via NVIDIA® OptiXTM

Opticks is an open source project that accelerates optical photon simulation by integrating NVIDIA GPU ray tracing, accessed via NVIDIA OptiX, with Geant4 toolkit based simulations. A single NVIDIA Turing architecture GPU has been measured to provide optical photon simulation speedup factors exceeding 1500 times single threaded Geant4 with a full JUNO analytic GPU geometry automatically translated from the Geant4 geometry. Optical physics processes of scattering, absorption, scintillator reemission and boundary processes are implemented within CUDA OptiX programs based on the Geant4 implementations. Wavelength-dependent material and surface properties as well as inverse cumulative distribution functions for reemission are interleaved into GPU textures providing fast interpolated property lookup or wavelength generation. Major recent developments enable Opticks to benefit from ray trace dedicated RT cores available in NVIDIA RTX series GPUs. Results of extensive validation tests are presented.

Fast and Cycle-Accurate Simulation of RTL NoC Designs Using Test-Driven Cellular Automata

Speeding up the register-transfer level (RTL) simulation of network-on-chip (NoC) is essential for design optimization under various use scenarios and parameters. One of the promising approaches for RTL NoC speedup is high-level modeling. Conventional high-level modeling approaches lead to an accuracy problem or modeling efforts that are caused by the absence of modeling framework or requiring in-depth knowledge of specific behaviors of target NoCs. To support cycle-accurate and formal high-level modeling framework, we propose a cellular automata (CA) modeling framework for RTL NoC. The CA abstracts detailed RTL NoC dynamics into the proposed high-level state transitions, which support flit transmission among CA components through dynamically changing flit paths based on the target RTL routing and arbitration algorithms. To prevent the meaningless execution of stable CA, the CA are designed to be triggered by state-change events. The proposed simulation engine asynchronously invokes CA to update their states and perform actions of flit transmissions or flit-path changes based on the state-decision result. To reduce the modeling difficulty, we provide a test environment that generates the state-transition rules for CA after monitoring the relationships between high-level states and leading actions under randomly injected packets during target RTL NoC simulations. Experiments demonstrate cycle-level functional homogeneity between RTL and the abstracted CA NoC models and significant simulation speedup.

Analytical Performance Models for NoCs with Multiple Priority Traffic Classes

Networks-on-chip (NoCs) have become the standard for interconnect solutions in industrial designs ranging from client CPUs to many-core chip-multiprocessors. Since NoCs play a vital role in system performance and power consumption, pre-silicon evaluation environments include cycle-accurate NoC simulators. Long simulations increase the execution time of evaluation frameworks, which are already notoriously slow, and prohibit design-space exploration. Existing analytical NoC models, which assume fair arbitration, cannot replace these simulations since industrial NoCs typically employ priority schedulers and multiple priority classes. To address this limitation, we propose a systematic approach to construct priority-aware analytical performance models using micro-architecture specifications and input traffic. Our approach decomposes the given NoC into individual queues with modified service time to enable accurate and scalable latency computations. Specifically, we introduce novel transformations along with an algorithm that iteratively applies these transformations to decompose the queuing system. Experimental evaluations using real architectures and applications show high accuracy of 97% and up to 2.5× speedup in full-system simulation.

Behavioral Modeling of Tunable I/O Drivers With Preemphasis Including Power Supply Noise

This article addresses the nonlinear behavioral modeling of tunable drivers with preemphasis including power supply noise. The proposed model relies on the use of state-aware weighting functions that control the transitions of the driver’s output stage for the scenarios where switched input logic states are shorter than the preemphasis duration, and the influence of supply voltage variation is considered. For the power supply noise analysis, the method is applied to multiple ports. Feedforward neural networks (FFNNs) are used to implement the state-aware weighting functions, and recurrent neural networks (RNNs) are used to capture the dynamic memory characteristics of driver’s ports. For tunable drivers in the state-of-the-art design covering features such as drive strength and preemphasis, a parameterized model that considers driver control parameters is presented. As a black-box approach, the resulting model protects intellectual property (IP). Practical industrial driver examples demonstrate the good accuracy, flexibility, and significant simulation speedup of the proposed model, which can facilitate the signal and power integrity (SIPI) analysis.

EPSim-C: A Parallel Epoch-Based Cycle-Accurate Microarchitecture Simulator Using Cloud Computing

Recently, computing platforms have been being configured on a large scale to satisfy the diverse requirements of emerging applications like big data and graph processing, neural network, speech recognition and so on. In these computing platforms, each computing node consists of a multicore, an accelerator, and a complex memory hierarchy, which are connected to other nodes using a variety of high-performance networks. Up to now, researchers have been using cycle-accurate simulators to evaluate the performance of computer systems in detail. However, the execution of the simulators, which models modern computing architecture for multi-core, multi-node, datacenter, memory hierarchy, new memory, and new interconnection, is too slow and infeasible; since the architecture has become more complex today, the complexity of the simulator is rapidly increasing. Therefore, it is seriously challenging to employ them in the research and development of next-generation computer systems. To solve this problem, we previously presented EPSim (Epoch-based Simulator), which defines epochs that can be run independently by dividing the simulation run into several sections and executes them in parallel on a multicore platform, resulting in only the limited simulation speedup. In this paper, to overcome the computing resource limitations on multi-core platforms, we propose a novel EPSim-C (EPSim on Cloud) simulator that extends EPSim and achieves higher performance using a cloud computing platform. EPSim-C is designed to perform the epoch-based executions in a massively parallel fashion by using MapReduce on Hadoop-based systems. According to our experiments, we have achieved a maximum speed of 87.0× and an average speed of 46.1× using 256 cores. As far as we know, EPSim-C is the only existing way to accelerate the cycle-accurate simulator on cloud platforms; thus, our significant performance enhancement allows researchers to model and research current and future cutting-edge computing platforms using real workloads.

Trough OpenMP Platform for Reducing Computational Time Cost in Underwater Landslide Simulation on Inclined Bottom

Simulation of underwater landslide becomes important, since underwater landslide phenomena is very dangerous in real life. One of the enormous disasters caused by this phenomena can be a Tsunami. Computer simulation of underwater landslide can reduce cost of time and money from conventional simulation (using laboratory). However, to obtain high resolution of computer simulation, large discrete points should be computed. In this paper, the numerical simulation of underwater landslide using two-layers shallow water equations (SWE) and OpenMP platform is elaborated. Here, the finite volume method framework using upwinding dispersive correction hydrostatic reconstruction (UDCHR) scheme is used. The results of numerical simulation is in a good agreement with the numerical simulation using Nasa-Vof2d numerical scheme. In parallel performance, speedup and efficiency of this numerical simulation are observed 2.8 times and 76% respectively at t=0.8 s final time simulation.

Modeling building resilience against extreme weather by integrated CityFFD and CityBEM simulations

In the past decade, urban building energy models have been developed to address the increasing concerns over energy consumption and greenhouse gas emission due to rapid urbanization and building resilience as a result of climate change. These models can estimate energy consumption, GHG emission and resilience response of buildings in an urban area, and evaluate retrofit strategies for architects, engineers, researchers and policy makers. It has been recognized that local microclimate and neighborhood effects play an important role in urban building energy modeling. Creating an urban building energy model also requires the collection of extensive building data, which is a time-consuming process. In this study, we developed an integrated platform by combining CityFFD (City Fast Fluid Dynamics), an urban-scale fast fluid dynamics model for microclimate modeling, and CityBEM (City Building Energy Model), a new urban building energy model with a library of 1700 building archetypes for facilitating urban model creation. Local aerodynamics and heat transfer information are exchanged between both models at each time step. Graphics processing unit computing is also applied to CityFFD for simulation speedup. The simulation of the 1971 Montreal snowstorm of the century was conducted as a case study of more than 1500 buildings of an island near Montreal, Canada for the investigation of their resilience against the three-day power outage due to the storm. Building retrofit analysis was also conducted to evaluate the added level of resilience. The results show that the proposed platform can produce high-resolution results of building thermal load, microclimate condition, and building behavior during weather extremes.

An extended finite volume model for implicit cohesive zone fracture propagation in a poroelastic medium

Models for fluid-driven fractures in a poroelastic medium involve the simultaneous simulation of multiple physical processes—diffusion of pore pressure, poroelastic stresses, fluid injection into a fractured porous medium, and fracture propagation. To simulate the above-mentioned physics, many algorithms and discretization techniques have been used in the past. The finite volume method has been gaining popularity for simulating solid mechanics problems. The discretization algorithms discussed in the past have used a segregated method for solving the poroelastic momentum balance, where iterations are necessary to obtain a converged solution for each component of the displacement vector. This segregated approach, when coupled with fluid-driven fracture propagation, can lead to excessive simulation times because of the coupled nature of the problem.In this study, an implicit formulation was designed to construct a linear system of equation for the components of the displacement vector to solve the poroelastic momentum balance equation (without iterating between components). Within this formulation, a fluid-driven fracture propagation model was implicitly incorporated using a cohesive zone approach. This methodology provided accurate solutions as shown by the validations in this paper where simulated results were compared with various well-known analytical solutions. The implicitness of the new model allowed significant improvements in computation speed when solving multi-physics problems. The simulation speed-ups were found to be 2 to 8 times when compared with the segregated method.

Shared Memory Architecture for Simulating Sediment-Fluid Flow by OpenMP

Simulation of fluid flow using Shallow water equations (SWE) and sediment movement below it using Exner equation is given. Both of the equations will be combined using splitting technique, in which SWE would be computed using Harten-Lax-van Leer and Einfeldt (HLLE) numerical flux, then Exner would be computed semi-implicitly. This paper elaborates the steps of constructing SWE-Exner model. To show the agreement of the scheme, two problems will be elaborated: (1) comparison between analytical solution and numerical solution, and (2) parallelism using OpenMP for Transcritical over a granular bump. The first problem is going to tell the discrete $L^{1}$-, $L^{2}$-, and $L^{\infty}$-norm error of the scheme, and the second one will show the simulation result, speedup, and efficiency of the scheme, which is around $56.44\%$.