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Optical solitons for Biswas-Arshed equation with multiplicative noise via Ito calculus using three integration algorithms

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OPTIK 2022年 258卷 168847-168847页

作者： Zayed, Elsayed M. E. Shohib, Reham M. A. Alngar, Mohamed E. M. Gepreel, Khaled A. Nofal, Taher A. Yildirim, Yakup Zagazig Univ Math Dept Fac Sci Zagazig 44519 Egypt Taif Univ Coll Sci Dept Math POB 11099 Taif 21944 Saudi Arabia Near East Univ Fac Arts & Sci Dept Math CY-99138 Nicosia Cyprus

The current paper studies optical solitons with the nonlinear stochastic Biswas-Arshed equation for the first time. Dark, bright, and singular solitons are presented via three integration technologies.

关键词： Multiplicative noise Solitons integration algorithms

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A semi-explicit integration algorithm with controllable numerical damping for real-time hybrid simulation

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STRUCTURES 2025年 74卷

作者： Lai, Zhenfeng Liu, Yanhui Tan, Ping Peng, Jinqiang Zhou, Fulin Guangzhou Univ Earthquake Engn Res & Test Ctr EERTC Guangzhou 510006 Peoples R China Minist Educ Key Lab Earthquake Resistance Earthquake Mitigat & Guangzhou 510006 Peoples R China Guangdong Prov Key Lab Earthquake Engn & Appl Tech Guangzhou 510006 Peoples R China

Real-time hybrid simulation (RTHS) is a cost-effective experimental method for evaluating the dynamic behavior of structures. In the numerical computation component of RTHS, the use of efficient, accurate, and stable integration algorithms is critical for its effective execution. This study presents a single-step semi-explicit integration algorithm SSE-alpha, designed to enhance the precision and robustness of numerical computations in RTHS. The numerical properties of the proposed algorithm, including stability, accuracy, and overshoot behavior, are evaluated. The results show that the SSE-alpha algorithm offers flexible and controllable numerical damping, offering unconditional stability for both linear and softened nonlinear systems. This algorithm features second-order accuracy and can effectively reduce or eliminate overshoot through parameter adjustment. The comparative analysis with the G-alpha, WBZ-alpha, and MKR-alpha algorithms demonstrates that the proposed algorithm exhibits superior stability, precision, computational efficiency, and numerical damping characteristics. Finally, the effectiveness and stability of the SSE-alpha algorithm are confirmed through its application to different structural systems in RTHS. This algorithm ensures improved real-time computational accuracy and stability for the assessment of structural systems, including critical infrastructure under seismic loading, contributing to advancements in structural dynamics.

关键词： Semi-explicit integration algorithms Real-time hybrid simulation Numerical damping Spectral radius Stability and accuracy

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Performance of explicit substepping integration scheme for complex constitutive models in finite element analysis

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COMPUTERS AND GEOTECHNICS 2023年第1期162卷

作者： Dong, Yuepeng Tech Univ Denmark Dept Environm & Resource Engn DK-2800 Lyngby Denmark

Advanced constitutive models for soils are critical to achieve reliable results in geotechnical analyses, but their implementation in finite element programs should be accurate, efficient, and robust. This paper describes the algorithm used to integrate a complex elastoplastic constitutive model for clays, the MIT-E3, in the finite element framework, followed by extensive evaluations. The explicit substepping scheme with different order of accuracy is adopted in the integration due to its simplicity, and also because of complexities in the model formulation. Several important issues are highlighted in the integration to improve the model performance in the analysis, (i) rigorous update of the void ratio, (ii) efficient intersection with the bounding surface, (iii) consistent correction of the drifted stress to the bounding surface, and (iv) consistently linearized tangent operator in the explicit substepping scheme. The numerical integration is verified by reproducing the stress-strain behaviour in single element tests, and also by checking the error behaviour with the order of accuracy of the integration method. The accuracy and efficiency of different methods in the integration are evaluated in a rigorous and consistent manner, which has practical implications for choosing suitable methods and parameters in the analysis. Good convergence rate can be achieved using the proposed consistently linearized tangent operator. The substepping scheme with error control is shown to be stable in the challenging geotechnical problems, while the efficiency is affected by the strain increment size which is problem dependent.

关键词： Constitutive models Finite element method integration algorithms Accuracy and efficiency

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Stock market information disclosure and risk management in the perspective of data fusion——Take market manipulation identification as an example

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Procedia Computer Science 2023年 221卷 1539-1546页

作者： Sihan Yao Aihua Li Zhidong Liu School of Management Science and Engineering Central University of Finance and Economics Beijing 100080 P.R. China School of Finance University of International Business and Economics Beijing 100105 P.R. China

The stock market, one of the most important trading platforms, has been subject to many market manipulation practices since its emergence. At present, the phenomenon of market manipulation has become an obstacle that restricts the development of the stock market. Based on the data fusion background, this paper conducts a study on the A-share listed companies publicly investigated and confirmed as market manipulation by CSRC in China from 2018-2022 as a manipulation sample under the perspective of fusion of data, model and decision, to provide theoretical support for regulators to identify market manipulation under the new trend. The results show that: ① Comparing with single financial data, different types of models respond to text indicators significantly differently. More than that, a reasonable addition of text dimensions can optimize the model performance; ② Comparing with a single base classifier, integrated models generally have better recognition performance. In addition, this effect can be deeply improved with the diversification of the base classifier.

关键词： data fusion market manipulation machine learning integration algorithms information disclosure

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Efficient recursive Adams-Bashforth methods in molecular dynamics simulations of N-body systems interacting through pairwise potentials

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MOLECULAR SIMULATION 2020年第16期46卷 1248-1254页

作者： Marti, Jordi Diaz, Bernat Tech Univ Catalonia Barcelona Tech Dept Phys Barcelona Spain Tech Univ Catalonia Barcelona Tech Fac Comp Sci Barcelona Spain

A recursive multistep Adams-Bashforth method applied to the Molecular Dynamics simulations of N-body systems interacting through pairwise force fields is introduced and analysed. Equations of motion are obtained using a set of Cartesian coordinates solved by means of an Adams-Bashforth numerical integration scheme of orders, which requires the iterative computation of function time derivatives. The proposed algorithm has been implemented using a programming approach that makes it possible to re-use a source code resulting in small codes, easy to maintain. Practical examples and benchmarks that illustrate the performance of these implementations are included. The study of its performance gives clues to evaluate its efficiency and precision. Numerical tests for a N-particle system are made on the equilibrium configuration of liquid argon near its triple point at 86.5 K and 0.021 angstrom(-3). In most cases, the algorithms here presented outperform those implemented traditionally as the Gear corrector-predictor or the Verlet family, leading to important savings in terms of total computation times and significantly increasing the numerical precision obtained with standard algorithms.

关键词： Recursive formulation Adams-Bashforth methods integration algorithms molecular dynamics

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A Generalized Backward Euler algorithm for the numerical integration of a viscous breakage model

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INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS 2019年第1期43卷 3-29页

作者： Marinelli, Ferdinando Buscarnera, Giuseppe Northwestern Univ Dept Civil & Environm Engn 2145 Sheridan Rd Evanston IL 60208 USA

This paper discusses the formulation and the numerical performance of a fully implicit algorithm used to integrate a rate-dependent model defined within a breakage mechanics framework. For this purpose, a Generalized Backward Euler (GBE) algorithm has been implemented according to two different linearization strategies: The former is derived by a direct linearization of the constitutive equations, while the latter introduces rate effects through a consistency parameter. The accuracy and efficiency of the GBE algorithm have been investigated by (1) performing material point analyses and (2) solving initial boundary value problems. In both cases, the overall performance of the underlying algorithm is inspected for a range of loading rates, thus simulating comminution from slow to fast dynamic problems. As the viscous response of the breakage model can be recast through a viscous nucleus function, the presented algorithm can be considered as a general framework to integrate constitutive equations relying on the overstress approach typical of Perzyna-like viscoplastic models.

关键词： continuum breakage mechanics finite element method integration algorithms Perzyna viscoplasticity rate effects

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Simplified Design of Dual Quaternion Strapdown Inertial Navigation integration algorithms

Simplified Design of Dual Quaternion Strapdown Inertial Navi...

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International Conference on Measurement, Instrumentation and Automation (ICMIA 2012)

作者： Lin Yu-rong Chen Liang Fu Zhen-xian Harbin Inst Technol Dept Control Sci & Engn Harbin 150001 Peoples R China

ISBN: (纸本)9783037855454

Dual quaternion navigation algorithm gain higher accuracy than traditional strapdown inertial navigation algorithm at the cost of real-time performance. In order to reduce tremendous computation amount of the former, a simplified design scheme for navigation integration algorithms is presented in this paper. First, based on update principle and computation rules of dual quaternion we separate rotational and translational increment information from dual quaternion increment, and deduce exact solutions defined by the spiral vector for thrust velocity increment, gravitational velocity increment and displacement increment. Then, considering characteristics of a strapdown inertial navigation system, implementation schemes of simplified integration algorithms for dual quaternion differential equations in three frames, including thrust velocity coordinates, gravitational velocity coordinates and position coordinates, are designed separately. Under the premise of ensuring the accuracy advantage of the original dual quaternion inertial navigation algorithm, the proposed simplified algorithm significantly improve the computational efficiency. This will lay favorable foundation for engineering realization of the dual quaternion strapdown inertial navigation algorithm.

关键词： Dual quatrenion integration algorithms Simplified design Thrust velocity Gravitational velocity

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Accelerating finite-rate chemical kinetics with coprocessors: Comparing vectorization methods on GPUs, MICs, and CPUs

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COMPUTER PHYSICS COMMUNICATIONS 2018年 226卷 18-29页

作者： Stone, Christopher P. Alferman, Andrew T. Niemeyer, Kyle E. Computat Sci & Engn LLC Athens GA 30605 USA Oregon State Univ Sch Mech Ind & Mfg Engn Corvallis OR 97331 USA

Accurate and efficient methods for solving stiff ordinary differential equations (ODES) are a critical component of turbulent combustion simulations with finite-rate chemistry. The ODEs governing the chemical kinetics at each mesh point are decoupled by operator-splitting allowing each to be solved concurrently. An efficient ODE solver must then take into account the available thread and instruction level parallelism of the underlying hardware, especially on many-core coprocessors, as well as the numerical efficiency. A stiff Rosenbrock and a nonstiff Runge-Kutta ODE solver are both implemented using the single instruction, multiple thread (SIMT) and single instruction, multiple data (SIMD) paradigms within OpenCL. Both methods solve multiple ODEs concurrently within the same instruction stream. The performance of these parallel implementations was measured on three chemical kinetic models of increasing size across several multicore and many-core platforms. Two separate benchmarks were conducted to clearly determine any performance advantage offered by either method. The first benchmark measured the run-time of evaluating the right-hand-side source terms in parallel and the second benchmark integrated a series of constant-pressure, homogeneous reactors using the Rosenbrock and Runge-Kutta solvers. The right-hand-side evaluations with SIMD parallelism on the host multicore Xeon CPU and many-core Xeon Phi co-processor performed approximately three times faster than the baseline multithreaded C++ code. The SIMT parallel model on the host and Phi was 13%-35% slower than the baseline while the SIMT model on the NVIDIA Kepler GPU provided approximately the same performance as the SIMD model on the Phi. The runtimes for both ODE solvers decreased significantly with the SIMD implementations on the host CPU (2.5-2.7x) and Xeon Phi coprocessor (4.7-4.9x) compared to the baseline parallel code. The SIMT implementations on the GPU ran 1.5-1.6 times faster than the baseline mult

关键词： Chemical kinetics integration algorithms Stiff ODEs SIMD GPU

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An investigation of GPU-based stiff chemical kinetics integration methods

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COMBUSTION AND FLAME 2017年第May.期179卷 312-324页

作者： Curtis, Nicholas J. Niemeyer, Kyle E. Sung, Chih-Jen Univ Connecticut Dept Mech Engn Storrs CT 06269 USA Oregon State Univ Sch Mech Ind & Mfg Engn Corvallis OR 97331 USA

A fifth-order implicit Runge-Kutta method and two fourth-order exponential integration methods equipped with Krylov subspace approximations were implemented for the GPU and paired with the analytical chemical kinetic Jacobian software pyJac. The performance of each algorithm was evaluated by integrating thermochemical state data sampled from stochastic partially stirred reactor simulations and compared with the commonly used CPU-based implicit integrator CVODE. We estimated that the implicit Runge-Kutta method running on a single Tesla C2075 GPU is equivalent to CVODE running on 12-38 Intel Xeon E5-4640 v2 CPU cores for integration of a single global integration time step of 10(-6)s with hydrogen and methane kinetic models. In the stiffest case studied-the methane model with a global integration time step of 10(-4)s-thread divergence and higher memory traffic significantly decreased GPU performance to the equivalent of CVODE running on approximately three CPU cores. The exponential integration algorithms performed more slowly than the implicit integrators on both the CPU and GPU. Thread divergence and memory traffic were identified as the main limiters of GPU integrator performance, and techniques to mitigate these issues were discussed. Use of a finite-difference Jacobian on the GPU-in place of the analytical Jacobian provided by pyJac-greatly decreased integrator performance due to thread divergence, resulting in maximum slowdowns of 7.11 - 240.96x;in comparison, the corresponding slowdowns on the CPU were just 1.39 - 2.61x, underscoring the importance of use of an analytical Jacobian for efficient GPU integration. Finally, future research directions for working towards enabling realistic chemistry in reactive-flow simulations via GPU/SIMT accelerated stiff chemical kinetics integration were identified.(C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

关键词： Chemical kinetics Stiff chemistry integration algorithms GPU SIMT

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Explicit solitons in the parabolic law nonlinear negative-index materials

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NONLINEAR DYNAMICS 2017年第1期88卷 595-607页

作者： Sonmezoglu, Abdullah Yao, Min Ekici, Mehmet Mirzazadeh, Mohammad Zhou, Qin Bozok Univ Dept Math Fac Sci & Arts TR-66100 Yozgat Turkey Wuhan Donghu Univ Sch Elect & Informat Engn Wuhan 430212 Peoples R China Univ Guilan Dept Engn Sci Fac Engn & Technol Rudsar Vajargah *** Iran

This paper deals with the existence of explicit ultra-short solitons in the negative-index materials with third-order dispersion and higher-order nonlinearities. Four integration algorithms, that are the improved modified extended tanh-function method, the extended trial equation method, the extended Jacobi elliptic function expansion method and the -expansion method, are employed to extract analytical traveling wave solutions. The presented results show that exact solitons can exist in this physical model.

关键词： Solitons Negative-index materials integration algorithms Traveling wave solutions

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