scholarly journals A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Omar Abu Arqub ◽  
Ahmad El-Ajou ◽  
A. Sami Bataineh ◽  
I. Hashim
Keyword(s):  
Exact Solution ◽  
Analytical Method ◽  
Taylor Expansion ◽  
Computational Cost ◽  
Test Problems ◽  
Analytic Method ◽  
Computational Results ◽  
Initial Value ◽  
Practical Usefulness ◽  
And Performance

A new analytic method is applied to singular initial-value Lane-Emden-type problems, and the effectiveness and performance of the method is studied. The proposed method obtains a Taylor expansion of the solution, and when the solution is polynomial, our method reproduces the exact solution. It is observed that the method is easy to implement, valuable for handling singular phenomena, yields excellent results at a minimum computational cost, and requires less time. Computational results of several test problems are presented to demonstrate the viability and practical usefulness of the method. The results reveal that the method is very effective, straightforward, and simple.

scholarly journals An efficient 4-step block method for solution of first order initial value problems via shifted chebyshev polynomial

2021 ◽  
Vol 1 (2) ◽  
pp. 25-36
Author(s):  
Isah O. ◽  
Salawu S. ◽  
Olayemi S. ◽  
Enesi O.
Keyword(s):  
Exact Solution ◽  
Initial Value Problems ◽  
Numerical Solutions ◽  
Test Problems ◽  
Block Method ◽  
Initial Value ◽  
Order Zero ◽  
First Order ◽  
Continuous Scheme ◽  
Shifted Chebyshev Polynomial

In this paper, we develop a four-step block method for solution of first order initial value problems of ordinary differential equations. The collocation and interpolation approach is adopted to obtain a continuous scheme for the derived method via Shifted Chebyshev Polynomials, truncated after sufficient terms. The properties of the proposed scheme such as order, zero-stability, consistency and convergence are also investigated. The derived scheme is implemented to obtain numerical solutions of some test problems, the result shows that the new scheme competes favorably with exact solution and some existing methods.

scholarly journals Emotion Recognition on Edge Devices: Training and Deployment

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4496
Author(s):  
Vlad Pandelea ◽  
Edoardo Ragusa ◽  
Tommaso Apicella ◽  
Paolo Gastaldo ◽  
Erik Cambria
Keyword(s):  
Emotion Recognition ◽  
Language Processing ◽  
Computational Cost ◽  
Sequential Learning ◽  
High Quality ◽  
Fast Training ◽  
Online Sequential Learning ◽  
And Performance ◽  
Resource Constrained Devices ◽  
Constrained Devices

Emotion recognition, among other natural language processing tasks, has greatly benefited from the use of large transformer models. Deploying these models on resource-constrained devices, however, is a major challenge due to their computational cost. In this paper, we show that the combination of large transformers, as high-quality feature extractors, and simple hardware-friendly classifiers based on linear separators can achieve competitive performance while allowing real-time inference and fast training. Various solutions including batch and Online Sequential Learning are analyzed. Additionally, our experiments show that latency and performance can be further improved via dimensionality reduction and pre-training, respectively. The resulting system is implemented on two types of edge device, namely an edge accelerator and two smartphones.

scholarly journals Torque modeling and characteristic analysis of electromagnetic piezoelectric hybrid-driven 3-degree-of-freedom motor

2018 ◽  
Vol 10 (10) ◽  
pp. 168781401880474 ◽  
Author(s):  
Zheng Li ◽  
Peng Guo ◽  
Ruihua Han ◽  
Qunjing Wang
Keyword(s):  
Analytical Method ◽  
Optimization Design ◽  
Basic Structure ◽  
Position Angle ◽  
Degree Of Freedom ◽  
Hybrid Drive ◽  
Characteristic Analysis ◽  
Drive Motor ◽  
And Performance ◽  
Air Gap Magnetic Field

The electromagnetic piezoelectric hybrid-driven 3-degree-of-freedom motor is a new multi-degree-of-freedom motor. To further analyze the torque characteristics of the electromagnetic piezoelectric hybrid-drive 3-degree-of-freedom motor. First, the principle and basic structure of the hybrid-drive motor are introduced, and the displacement and pressure distribution of the stator–rotor contact surface are obtained by analytical method. Based on this, the torque model of the piezoelectric stator-drive motor is obtained. Then, the air-gap magnetic field model of the permanent magnet rotor is obtained by analytical method, and the electromagnetic stator-torque model is obtained. Finally, the torque model of the electromagnetic piezoelectric hybrid-drive 3-degree-of-freedom motor is established by vector synthesis. The effects of piezoelectric stator mounting position angle, stator–rotor contact materials, and preload on motor torque are analyzed by simulation. The advantages of electromagnetic piezoelectric hybrid drive are analyzed, and the rationality of the model is preliminarily verified. It lays the foundation for further optimization design and performance improvement of electromagnetic piezoelectric hybrid-drive 3-degree-of-freedom motor.

scholarly journals A reduced order approach for probabilistic inversions of 3-D magnetotelluric data I: general formulation

2020 ◽  
Vol 223 (3) ◽  
pp. 1837-1863
Author(s):  
M C Manassero ◽  
J C Afonso ◽  
F Zyserman ◽  
S Zlotnik ◽  
I Fomin
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Forward Problem ◽  
Parallel Structure ◽  
Data Sets ◽  
Magnetotelluric Data ◽  
Reduced Order ◽  
Mcmc Algorithms ◽  
Simulation Based ◽  
And Performance

SUMMARY Simulation-based probabilistic inversions of 3-D magnetotelluric (MT) data are arguably the best option to deal with the nonlinearity and non-uniqueness of the MT problem. However, the computational cost associated with the modelling of 3-D MT data has so far precluded the community from adopting and/or pursuing full probabilistic inversions of large MT data sets. In this contribution, we present a novel and general inversion framework, driven by Markov Chain Monte Carlo (MCMC) algorithms, which combines (i) an efficient parallel-in-parallel structure to solve the 3-D forward problem, (ii) a reduced order technique to create fast and accurate surrogate models of the forward problem and (iii) adaptive strategies for both the MCMC algorithm and the surrogate model. In particular, and contrary to traditional implementations, the adaptation of the surrogate is integrated into the MCMC inversion. This circumvents the need of costly offline stages to build the surrogate and further increases the overall efficiency of the method. We demonstrate the feasibility and performance of our approach to invert for large-scale conductivity structures with two numerical examples using different parametrizations and dimensionalities. In both cases, we report staggering gains in computational efficiency compared to traditional MCMC implementations. Our method finally removes the main bottleneck of probabilistic inversions of 3-D MT data and opens up new opportunities for both stand-alone MT inversions and multi-observable joint inversions for the physical state of the Earth’s interior.

scholarly journals A Methodology to Evaluate the Reliability Impact of the Replacement of Welded Components by Additive Manufacturing Spare Parts

Metals ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 932 ◽  
Author(s):  
Armando Coro ◽  
Luis María Macareno ◽  
Josu Aguirrebeitia ◽  
Luis Norberto López de Lacalle
Keyword(s):  
Additive Manufacturing ◽  
Computational Cost ◽  
Reliability Function ◽  
Spare Parts ◽  
Jet Engine ◽  
First Order ◽  
Propagation Analysis ◽  
Reliability Method ◽  
And Performance ◽  
Inspection Scheduling

This article shows a method for inspection scheduling of structures made by additive manufacturing, derived from reliability function evaluations and overhaul inspection findings. The routine was an adaption of an existing method developed by the authors for welded components; in this latter case, the routine used a stochastic defect-propagation analysis for pores and lack of fusion defects of additive manufacturing process, instead of the weld liquation crack. In addition, the authors modified the specific stress-intensity factor for welded components to consider additive manufacturing-related material property variability, defect distributions, flaw-inspection capabilities, and component geometry. The proposed routine evaluated the failure rate and inspection intervals using the first-order reliability method (FORM + Fracture) to alleviate the computational cost of probabilistic defect-propagation analysis. The proposed method is one of the first applying reliability concepts to additive manufacturing (AM) components. This is an important milestone, since in 10 years, additive manufacturing is to be used for 30% of the components in aeroengines. This paper presents an example comparing the reliability and cost of a jet engine, with components either made by additive manufacturing or welded parts; in the process, the reliability AM-key features are found, and overhaul schedules of an airplane fleet made with AM components are defined. The simplicity and performance demonstrated in the comparison make the proposed method a powerful engineering tool for additive manufacturing assessment in aeronautics.

An adaptive sparse polynomial-chaos technique based on anisotropic indices

2020 ◽  
Vol 39 (3) ◽  
pp. 691-707
Author(s):  
Christos Salis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros Zygiridis
Keyword(s):  
Polynomial Chaos ◽  
Computational Cost ◽  
Uncertainty Assessment ◽  
Design Parameters ◽  
Test Problems ◽  
Content Type ◽  
Sparse Polynomial ◽  
Index Sets ◽  
The Mean ◽  
Expansion Coefficients

Purpose The fabrication of electromagnetic (EM) components may induce randomness in several design parameters. In such cases, an uncertainty assessment is of high importance, as simulating the performance of those devices via deterministic approaches may lead to a misinterpretation of the extracted outcomes. This paper aims to present a novel heuristic for the sparse representation of the polynomial chaos (PC) expansion of the output of interest, aiming at calculating the involved coefficients with a small computational cost. Design/methodology/approach This paper presents a novel heuristic that aims to develop a sparse PC technique based on anisotropic index sets. Specifically, this study’s approach generates those indices by using the mean elementary effect of each input. Accurate outcomes are extracted in low computational times, by constructing design of experiments (DoE) which satisfy the D-optimality criterion. Findings The method proposed in this study is tested on three test problems; the first one involves a transmission line that exhibits several random dielectrics, while the second and the third cases examine the effects of various random design parameters to the transmission coefficient of microwave filters. Comparisons with the Monte Carlo technique and other PC approaches prove that accurate outcomes are obtained in a smaller computational cost, thus the efficiency of the PC scheme is enhanced. Originality/value This paper introduces a new sparse PC technique based on anisotropic indices. The proposed method manages to accurately extract the expansion coefficients by locating D-optimal DoE.

scholarly journals A New Algorithm for Solving Terminal Value Problems of q-Difference Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yong-Hong Fan ◽  
Lin-Lin Wang
Keyword(s):  
Exact Solution ◽  
Numerical Methods ◽  
Error Estimate ◽  
Numerical Solution ◽  
Numerical Method ◽  
Difference Equations ◽  
Initial Value Problems ◽  
Convergence Speed ◽  
Initial Value ◽  
Delta Derivatives

We propose a new algorithm for solving the terminal value problems on a q-difference equations. Through some transformations, the terminal value problems which contain the first- and second-order delta-derivatives have been changed into the corresponding initial value problems; then with the help of the methods developed by Liu and H. Jafari, the numerical solution has been obtained and the error estimate has also been considered for the terminal value problems. Some examples are given to illustrate the accuracy of the numerical methods we proposed. By comparing the exact solution with the numerical solution, we find that the convergence speed of this numerical method is very fast.

Diagonal Quadratic Approximation for Parallelization of Analytical Target Cascading

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Yanjing Li ◽  
Zhaosong Lu ◽  
Jeremy J. Michalek
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Descent Method ◽  
Quadratic Approximation ◽  
Test Problems ◽  
Analytical Target Cascading ◽  
Decomposition Approach ◽  
Diagonal Quadratic Approximation ◽  
Target Cascading ◽  
Nested Loop

Analytical target cascading (ATC) is an effective decomposition approach used for engineering design optimization problems that have hierarchical structures. With ATC, the overall system is split into subsystems, which are solved separately and coordinated via target/response consistency constraints. As parallel computing becomes more common, it is desirable to have separable subproblems in ATC so that each subproblem can be solved concurrently to increase computational throughput. In this paper, we first examine existing ATC methods, providing an alternative to existing nested coordination schemes by using the block coordinate descent method (BCD). Then we apply diagonal quadratic approximation (DQA) by linearizing the cross term of the augmented Lagrangian function to create separable subproblems. Local and global convergence proofs are described for this method. To further reduce overall computational cost, we introduce the truncated DQA (TDQA) method, which limits the number of inner loop iterations of DQA. These two new methods are empirically compared to existing methods using test problems from the literature. Results show that computational cost of nested loop methods is reduced by using BCD, and generally the computational cost of the truncated methods is superior to the nested loop methods with lower overall computational cost than the best previously reported results.

The Variational IterationMethod for Finding Exact Solution of Nonlinear Gas Dynamics Equations

2011 ◽  
Vol 66 (3-4) ◽  
pp. 161-164 ◽  
Author(s):  
Hossein Jafari ◽  
Ch. Chun ◽  
C.M. Khalique
Keyword(s):  
Exact Solution ◽  
Nonlinear Equations ◽  
Analytical Solutions ◽  
Analytical Method ◽  
Iteration Method ◽  
Gas Dynamics ◽  
Variational Iteration Method ◽  
Gas Dynamics Equations ◽  
Exact Analytical Solutions ◽  
Gas Dynamics Equation

The variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method to solve nonlinear equations. In this paper, a modified VIM is introduced to accelerate the convergence of VIM and it is applied for finding exact analytical solutions of nonlinear gas dynamics equation.

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