Integration Step Research Articles

High-Performance Computing Probabilistic Fracture Mechanics Implementation for Gas Turbine Rotor Disks on Distributed Architectures Including Graphics Processing Units

Abstract We present an efficient Monte Carlo-based probabilistic fracture mechanics simulation implementation for heterogeneous high-performance computing (HPC) architectures including central processing units (CPUs) and graphics processing units (GPUs). The specific application focuses on large heavy-duty gas turbine rotor components for the energy sector. A reliable probabilistic risk quantification requires the simulation of millions to billions of Monte Carlo (MC) samples. We apply a modified Runge–Kutta algorithm in order to solve numerically the fatigue crack growth for this large number of cracks for varying initial crack sizes, locations, material, and service conditions. This compute intensive simulation has already been demonstrated to perform efficiently and scalable on parallel and distributed HPC architectures including hundreds of CPUs utilizing the message passing interface (MPI) paradigm. In this work, we go a step further and include GPUs in our parallelization strategy. We develop a load distribution scheme to share one or more GPUs on compute nodes distributed over a network. We detail technical challenges and solution strategies in performing the simulations on GPUs efficiently. We show that the key computation of the modified Runge–Kutta integration step speeds up over two orders of magnitude on a typical GPU compared to a single threaded CPU. This is supported by our use of GPU textures for efficient interpolation of multidimensional tables utilized in the implementation. We demonstrate weak and strong scaling of our GPU implementation, i.e., that we can efficiently utilize a large number of GPUs/CPUs in order to solve for more MC samples, or reduce the computational turn-around time, respectively. On seven different GPUs spanning four generations, the presented probabilistic fracture mechanics simulation tool ProbFM achieves a speed-up ranging from 16.4× to 47.4× compared to single threaded CPU implementation.

An efficient dynamic modeling and simulation method of a cable-constrained synchronous rotating mechanism for continuum space manipulator

Continuum space manipulators have advantages in working in the confined spaces to conduct some fine operating tasks for high-value malfunctioning satellites, while Cable-Constrained Synchronous Rotating Mechanism (CCSRM) is a new mechanical structure for continuum manipulators to improve their stiffness and reduce the motor numbers. However, the dynamic equations of manipulators with CCSRM have stiff problems, which reduce the calculation efficiency. This paper proposes an efficient dynamic modeling and simulation method for continuum space manipulators with CCSRM. The rotations of rigid links of the manipulator are described by quaternion parameters, and the dynamic equations of the system are obtained by using Lagrange equations of the first kind. The connecting cables of the CCSRM are modeled by linear torsional spring-dampers. The stiff problems are modified by a model smoothing method to reduce the high-frequency components of the motion, after which a relatively much larger integration step can be taken, which can significantly improve the calculation efficiency. Finally, two numerical examples are provided as demonstrative applications. The numerical results show that the proposed method can improve the calculation efficiency by two or three orders of magnitude and realize real-time simulation.

Intensity patterns at the peaks of brain activity in fMRI and PET are highly correlated with neural models of spatial integration.

Spatial integration during the brain's cognitive activity prompts changes in energy used by different neuroglial populations. Nevertheless, the organisation of such integration in 3D ‐brain activity remains undescribed from a quantitative standpoint. In response, we applied a cross‐correlation between brain activity and integrative models, which yielded a deeper understanding of information integration in functional brain mapping. We analysed four datasets obtained via fundamentally different neuroimaging techniques (functional magnetic resonance imaging [fMRI] and positron emission tomography [PET]) and found that models of spatial integration with an increasing input to each step of integration were significantly more correlated with brain activity than models with a constant input to each step of integration. In addition, marking the voxels with the maximal correlation, we found exceptionally high intersubject consistency with the initial brain activity at the peaks. Our method demonstrated for the first time that the network of peaks of brain activity is organised strictly according to the models of spatial integration independent of neuroimaging techniques. The highest correlation with models integrating an increasing at each step input suggests that brain activity reflects a network of integrative processes where the results of integration in some neuroglial populations serve as an input to other neuroglial populations.

Automated constitutive modeling of isotropic hyperelasticity based on artificial neural networks

Herein, an artificial neural network (ANN)-based approach for the efficient automated modeling and simulation of isotropic hyperelastic solids is presented. Starting from a large data set comprising deformations and corresponding stresses, a simple, physically based reduction of the problem’s dimensionality is performed in a data processing step. More specifically, three deformation type invariants serve as the input instead of the deformation tensor itself. In the same way, three corresponding stress coefficients replace the stress tensor in the output layer. These initially unknown values are calculated from a linear least square optimization problem for each data tuple. Using the reduced data set, an ANN-based constitutive model is trained by using standard machine learning methods. Furthermore, in order to ensure thermodynamic consistency, the previously trained network is modified by constructing a pseudo-potential within an integration step and a subsequent derivation which leads to a further ANN-based model. In the second part of this work, the proposed method is exemplarily used for the description of a highly nonlinear Ogden type material. Thereby, the necessary data set is collected from virtual experiments of discs with holes in pure plane stress modes, where influences of different loading types and specimen geometries on the resulting data sets are investigated. Afterwards, the collected data are used for the ANN training within the reduced data space, whereby an excellent approximation quality could be achieved with only one hidden layer comprising a low number of neurons. Finally, the application of the trained constitutive ANN for the simulation of two three-dimensional samples is shown. Thereby, a rather high accuracy could be achieved, although the occurring stresses are fully three-dimensional whereas the training data are taken from pure two-dimensional plane stress states.

Fast sixth-order algorithm based on the generalized Cayley transform for the Zakharov-Shabat system associated with nonlinear Schrodinger equation

The nonlinear Schrödinger equation (NLSE) is widely used in telecommunication applications, since it allows one to describe the propagation of pulses in an optical fiber. Recently some new approaches based on the nonlinear Fourier transform (NFT) have been actively explored to compensate for fiber nonlinearity and to exceed the limitations of nonlinearity-imposed limits of linear transmission methods. Despite the fact that the numerical solution of NLSE is a general problem, nevertheless, the optical community has been focusing on this issue. Improving the accuracy of the NFT algorithms remains an urgent problem in optics. In particular, it is important to increase the approximation order of the methods, especially in problems where it is necessary to analyze the structure of complex waveforms. To correctly describe them and their spectral parameters, more accurate and fast numerical methods are needed.We propose a novel general approach for constructing sixth-order (with respect to an integration step) finite-difference schemes for first-order linear differential systems. These schemes are based on the generalized Cayley transform and include exponential integrators as a special case. If the system has a time-dependent skew-hermitian matrix then the schemes conserve the quadratic first integral automatically. Then we apply our method to solve the direct spectral problem for the Zakharov-Shabat system. New schemes with fractional rational transition matrix allow the use of fast algorithms to solve the initial problem for a large number of values of the spectral parameter.

Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

The increasing complexity of advanced devices and systems increases the scale of mathematical models used in computer simulations. Multiparametric analysis and study on long-term time intervals of large-scale systems are computationally expensive. Therefore, efficient numerical methods are required to reduce time costs. Recently, semi-explicit and semi-implicit Adams–Bashforth–Moulton methods have been proposed, showing great computational efficiency in low-dimensional systems simulation. In this study, we examine the numerical stability of these methods by plotting stability regions. We explicitly show that semi-explicit methods possess higher numerical stability than the conventional predictor–corrector algorithms. The second contribution of the reported research is a novel algorithm to generate an optimized finite-difference scheme of semi-explicit and semi-implicit Adams–Bashforth–Moulton methods without redundant computation of predicted values that are not used for correction. The experimental part of the study includes the numerical simulation of the three-body problem and a network of coupled oscillators with a fixed and variable integration step and finely confirms the theoretical findings.

Comparison of numerical integration methods for calculating diffraction of a plane electromagnetic wave by a rectangular aperture

We discuss features of the calculation of a Fraunhofer integral by traditional quadrature numerical integration methods and a special collocation Levin method when calculating the diffraction of a plane electromagnetic wave by a rectangular aperture. For the quadrature numerical integration methods, a criterion for the assessment of the integration step is derived depending on the screen size and required calculation accuracy. Advantages of the use of the special collocation Levin method in comparison with the traditional quadrature numerical integration methods are shown.

Hopfield neuronal network of fractional order: A note on its numerical integration

In this paper, the commensurate fractional-order variant of an Hopfield neuronal network is analyzed. The system is integrated with the ABM method for fractional-order equations. Beside the standard stability analysis of equilibria, the divergence of fractional order is proposed to determine the instability of the equilibria. The bifurcation diagrams versus the fractional order, and versus one parameter, reveal a strange phenomenon suggesting that the bifurcation branches generated by initial conditions outside neighborhoods of unstable equilibria are spurious sets although they look similar with those generated by initial conditions close to the equilibria. These spurious sets look ``delayed'' in the considered bifurcation scenario. Once the integration step-size is reduced, the spurious branches maintain their shapes but tend to the branches obtained from initial condition within neighborhoods of equilibria. While the spurious branches move once the integration step size reduces, the branches generated by the initial conditions near the equilibria maintain their positions in the considered bifurcation space. This phenomenon does not depend on the integration-time interval, and repeats in the parameter bifurcation space.

A Recursive Legendre Polynomial Analytical Integral Method for the Fast and Efficient Modelling Guided Wave Propagation in Rectangular Section Bars of Orthotropic Materials

Ultrasonic guided waves are widely used in non-destructive testing (NDT), and complete guided wave dispersion, including propagating and evanescent modes in a given waveguide, is essential for NDT. Compared with an infinite plate, the finite lateral width of a rectangular bar introduces a greater density of modes, and the dispersion solutions become more complicated. In this study, a recursive Legendre polynomial analytical integral (RLPAI) method is presented to calculate the dispersion behaviours of guided waves in rectangular bars of orthotropic materials. The existing polynomial method involves a large number of numerical integration steps, and it is often computationally costly to compute these integrals. The presented RLPAI method uses analytical integration instead of numerical integration, thus leading to a significant improvement in the computational speed. The results are compared with those published previously to validate our method, and the computational efficiency is discussed. The full three-dimensional dispersion curves are plotted. The dispersion characteristics of propagating and evanescent waves are investigated in various rectangular bars. The influences of different width-to-thickness ratios on the dispersion curves of four types of low-order modes for a rectangular bar of an orthotropic composite are illustrated.

RESEARCH OF TRANSIENT PROCESSES OF PRESSURE CHANGE WHEN OPERATING A HYDRAULIC SYSTEM WITH FOUR CONNECTED HYDRAULIC MOTORS

The publication is devoted to the study of the quality of the hydraulic system with four series-connected hydraulic motors. These hydraulic systems can be used to drive the working bodies of agricultural machines, have significant advantages in their layout, but at the same time and disadvantages, the elimination of which requires a detailed study of the processes occurring during the operation of this type of system. The analysis of the previous works of scientists in this area allows us to conclude that it is possible to conduct theoretical research in this direction. A mathematical model of the proposed hydraulic system has been developed, which takes into account the effect of external load on the shafts of hydraulic motors, the inertia of the system, the effect of leaks from the connections of the elements of the hydraulic system and possible overflows of the working fluid from the high-pressure zone to the low-pressure zone. At this stage, wave processes occurring in the cavities of the hydraulic system were not taken into account. The solution of the resulting system of differential equations was carried out using the Runge-Kutta-Feldberg method with automatic change of the integration step in the mathematical package MathCad. The resulting transient processes were analyzed for the amplitude of pressure surges and the frequency of its change. Carrying out this analysis allows you to obtain comprehensive information about the nature of transient processes in the hydraulic system in order to find such a ratio of design and technological parameters, in which the system under study met the requirements regarding the quality of work as part of a technological machine. During the research, special attention was paid to the processes occurring at the moment of starting the hydraulic system, and the moment of application of the technological load.

An adaptive multi-temperature isokinetic method for the RVE generation of particle reinforced heterogeneous materials, Part I: Theoretical formulation and computational framework

A new computational generation method for high-fidelity representative volume elements (RVEs) composed of particle reinforced materials is proposed, being coined AMINO (Adaptive Multi-temperature Isokinetic Method). This geometrical time-driven molecular dynamic method can effectively deal with several types of particles and microstructure descriptors, accounting for two main innovative features: (1) an adaptive time integration step scheme and (2) a multi-temperature isokinetic thermostat. The method does not require cumbersome parameters to be calibrated and can handle periodic boundary conditions, typically employed in designing and modeling heterogeneous materials. It fulfills the requirements to be integrated into the recent paradigm of data-driven material design frameworks and opens new avenues to create new materials. Part I of this paper is focused on the theoretical formulation of the proposed method and its computational implementation. Part II is dedicated to the statistical analysis and the numerical assessment of the method for the computationally generated microstructures.

Correction: The Utilisation of Reduced Kinetics by Local Self‑Similarity Tabulation Approach in 3D Turbulent Reactive Flow Simulation with LES and TPDF

Combustion simulations with high fidelity turbulence models and detailed chemistry may suffer from high computational power requirements due to the combined cost of time-scale dissipation and small integration steps. Such a limitation can be avoided by employing a hybrid reaction mechanism reduction method called local self-similarity tabulation (LS2T). LS2T directly solves several dominant species reactions and incorporates the effects of other species on dominant ones by data retrieval from pre-calculated tables. This paper demonstrates the application of LS2T method to a 3D combustion simulation of Sandia Flame-D. The combustion simulation uses large eddy simulation as turbulence solver and transported probability density function for species transport, to increase the accuracy of the simulation and avoid the use of any additional reaction model. The results show that by use of LS2T method, it is possible to maintain high accuracy and generate results similar to detailed chemistry of methane combustion while maintaining an acceptable computational effort.

Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control

We develop a new operator splitting formulation for the simulation of corotated linearly elastic solids with Smoothed Particle Hydrodynamics (SPH). Based on the technique of Kugelstadt et al. [2018] originally developed for the Finite Element Method (FEM), we split the elastic energy into two separate terms corresponding to stretching and volume conservation, and based on this principle, we design a splitting scheme compatible with SPH. The operator splitting scheme enables us to treat the two terms separately, and because the stretching forces lead to a stiffness matrix that is constant in time, we are able to prefactor the system matrix for the implicit integration step. Solid-solid contact and fluid-solid interaction is achieved through a unified pressure solve. We demonstrate more than an order of magnitude improvement in computation time compared to a state-of-the-art SPH simulator for elastic solids. We further improve the stability and reliability of the simulation through several additional contributions. We introduce a new implicit penalty mechanism that suppresses zero-energy modes inherent in the SPH formulation for elastic solids, and present a new, physics-inspired sampling algorithm for generating high-quality particle distributions for the rest shape of an elastic solid. We finally also devise an efficient method for interpolating vertex positions of a high-resolution surface mesh based on the SPH particle positions for use in high-fidelity visualization.

REVIEW OF CITY PARKS IN TERMS OF DISABLED RIGHTS

The creation and presentation of independent and individual spaces for disabled individuals is the most important step of social integration. The main purpose of this report is to investigate whether some city parks in Turkey are suitable or not for the use of disabled individuals. This descriptive research includes the perception of disabled individuals about the city parks in Hatay, Şanlıurfa and Gaziantep provinces. Individuals with disabilities assessed the structure of city parks, ease of use, ergonomics and basic needs with basic 22-questions. The questions focused on respondents' experiences with specific destinations and environmental barriers. 150 disabled individuals, 53 from Hatay, 53 from Şanlıurfa and 44 from Gaziantep, were included in the study. Participants; 29.3% were using wheelchairs, 34% were using electric wheelchairs, 30% were using crutches and 6.7% were not using assistive devices. As a result of the study, it was seen that the parks were not convenient and useful for the disabled individuals. Deficiencies in city parks can avoid evaluating and ensuring the leisure time activities, social compliance and exercise activities for disabled individuals. Thus, we think that these environments can maximize opportunities for leisure activities and social participation by individuals with lifelong disabilities.

Targeting the Integrated Stress Response Kinase GCN2 to Modulate Retroviral Integration.

Multiple viral targets are now available in the clinic to fight HIV infection. Even if this targeted therapy is highly effective at suppressing viral replication, caregivers are facing growing therapeutic failures in patients due to resistance, with or without treatment-adherence glitches. Accordingly, it is important to better understand how HIV and other retroviruses replicate in order to propose alternative antiviral strategies. Recent studies have shown that multiple cellular factors are implicated during the integration step and, more specifically, that integrase can be regulated through post-translational modifications. We have shown that integrase is phosphorylated by GCN2, a cellular protein kinase of the integrated stress response, leading to a restriction of HIV replication. In addition, we found that this mechanism is conserved among other retroviruses. Accordingly, we developed an in vitro interaction assay, based on the AlphaLISA technology, to monitor the integrase-GCN2 interaction. From an initial library of 133 FDA-approved molecules, we identified nine compounds that either inhibited or stimulated the interaction between GCN2 and HIV integrase. In vitro characterization of these nine hits validated this pilot screen and demonstrated that the GCN2-integrase interaction could be a viable solution for targeting integrase out of its active site.

Research on associated motion simulation method and platform of control rod driving mechanism

The motion simulation analysis of the control rod drive mechanism is a typical multi-disciplinary cross-coupling problem covering electromagnetic field, flow field, and dynamic field. Ensuring effective simulation accuracy is an important advance for accurately predicting the reliability of nuclear reactors. In this paper, a multi-disciplinary co-simulation method is proposed based on time unit differentiation, which solves the coupling problem of parameters by micro-element thought. It can avoid affecting the accuracy of simulation results due to the inequality of multi-disciplinary parameters in the co-simulation process. This paper takes the nuclear reactor control rod drive mechanism as the verification object. The multi-disciplinary co-simulation platform in Isight is built based on the co-simulation method. By differentiating the overall process of multidisciplinary co-simulation according to time unit and using the same simulation time interval for each discipline, the Newmark method is used to determine the minimum simulation time integration step of each discipline. The multi-field co-simulation is carried out including electromagnetic field, flow field, gravitational field, and motion field of the driving mechanism in the working process. Through comparison with the actual measurement results, the simulation results have an error within 5%, which is better than existing motion simulation results of driving mechanism.

Application Of Seeding Crystallization as a Pre-Treatment Stage for The Reduction of Scaling Tendency of Seawater Feed to Thermal Desalination Units

Objective: The fouling inhibition in seawater desalination and scale control using crystallization with calcite seeds is evaluated experimentally in this study. Methods: The growth kinetic parameters are determined experimentally, correlated and discussed at different operating conditions. Supersaturation levels represent driving force behind the growth of crystals, which is influenced directly by seawater pH values and temperatures. Results: Results indicate that the initial pH value of seawater must be controlled to be in the range (8-9) and calcite seeds will not have the potential to start the growth process in seawater at the normal pH (7.36). The growth kinetic parameters are determined from the measured desupersaturation curves. Conclusion: It is found that the growth process of calcite is controlled by the surface integration step. The growth rate of calcite increases with increasing temperature and seeding ratio (up to 1 g/L), while it decreases with increasing the salinity of seawater.

Simulation of Deformations of Pre-Stressed Steel Trusses in Emergency Situations

Purpose of research is to make methodology and algorithm for finite element modeling in a single computational scheme of deformation of flat steel trusses, previously stressed using high-strength ropes, in accordance with the chronology of impacts on the object in the form of prestresses, normative loads and emergency destruction of one of the bearing elements.Methods. The solution of the problem is carried out in geometrically nonlinear staging using numerical integration based on Newmark approach with the construction of equilibrium equations of the finite element model of the structure in a deformed state at each integration step. Structural nonlinearity related to structural restructuring and consideration of ropes operation for tension only is described. The application of gravity forces of the carrier system, sequential introduction of tightening and their prestress, the application of payload and emergency impact in the form of instantaneous local destruction are traced. Before failure occurs, static loading condition is simulated using dynamic relaxation method. Methodology of accounting within numerical integration of emergency impact is formulated by application of dummy forces, values of which are calculated in excluded structural element before its destruction.Results. Performance of presented computational procedure is illustrated by the example of a flat steel truss calculation with a span (54 m), including two ropes. Object behavior is considered considering the break of one of the ropes subjected to preliminary stress. It was revealed that the investigated emergency does not lead to the destruction of the second rope and the occurrence of plastic deformations in the truss rods.Conclusion: Completed developments can be used to ensure the survivability of pre-stressed steel trusses under beyond design basis effects, leading to the destruction of individual structural elements.

Nonconverged Constraints Cause Artificial Temperature Gradients in Lipid Bilayer Simulations.

Molecular dynamics (MD) simulations have become an indispensable tool to investigate phase separation in model membrane systems. In particular, simulations based on coarse-grained (CG) models have found widespread use due to their increased computational efficiency, allowing for simulations of multicomponent lipid bilayers undergoing phase separation into liquid-ordered and liquid-disordered domains. Here, we show that a significant temperature difference between molecule types can artificially arise in CG MD membrane simulations with the standard Martini simulation parameters in GROMACS. In particular, the linear constraint solver (LINCS) algorithm does not converge with its default settings, resulting in serious temperature differences between molecules in a time step-dependent manner. We demonstrate that the underlying reason for this behavior is the presence of highly constrained moieties, such as cholesterol. Their presence can critically impact numerous structural and dynamic membrane properties obtained from such simulations. Furthermore, any preference of these molecules toward a certain membrane phase can lead to spatial temperature gradients, which can amplify the degree of phase separation or even induce it in compositions that would otherwise mix well. We systematically investigated the effect of the integration time step and LINCS settings on membrane properties. Our data show that for cholesterol-containing membranes, a time step of 20 fs should be combined with at least lincs_iter = 2 and lincs_order = 12, while using a time step of 30 fs requires at least lincs_iter = 3 and lincs_order = 12 to bring the temperature differences to a level where they do not perturb central membrane properties. Moreover, we show that in cases where stricter LINCS settings are computationally too demanding, coupling the lipids in multiple groups to the temperature bath offers a practical workaround to the problem, although the validity of this approach should be further verified. Finally, we show that similar temperature gradients can also emerge in atomistic simulations using the CHARMM force field in combination with settings that allow for a 5 fs integration step.

A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation.

In a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient coupling algorithm for the two scales. Furthermore, the consideration of dynamic changes of muscle stiffness caused by the cross-bridge activity of motor proteins have not been well established in continuum mechanics. To overcome these issues, we propose a multiple time step scheme called the multiple step active stiffness integration scheme (MusAsi) for the coupling of Monte Carlo (MC) multiple steps and an implicit finite element (FE) time integration step. The method focuses on the active tension stiffness matrix, where the active tension derivatives concerning the current displacements in the FE model are correctly integrated into the total stiffness matrix to avoid instability. A sensitivity analysis of the number of samples used in the MC model and the combination of time step sizes confirmed the accuracy and robustness of MusAsi, and we concluded that the combination of a 1.25 ms FE time step and 0.005 ms MC multiple steps using a few hundred motor proteins in each finite element was appropriate in the tradeoff between accuracy and computational time. Furthermore, for a biventricular FE model consisting of 45,000 tetrahedral elements, one heartbeat could be computed within 1.5 h using 320 cores of a conventional parallel computer system. These results support the practicality of MusAsi for uses in both the basic research of the relationship between molecular mechanisms and cardiac outputs, and clinical applications of perioperative prediction.