APPLICATION OF THE POLYNOMIAL INTERPOLATION METHOD FOR DETERMINING PERFORMANCE CHARACTERISTICS OF A DIESEL ENGINE

2014 ◽  
Vol 21 (1) ◽  
pp. 157-168 ◽  
Author(s):  
Tomasz Stoeck ◽  
Karol Franciszek Abramek
Keyword(s):  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Sufficient Accuracy ◽  
Performance Characteristics ◽  
Combustion Engines ◽  
Lagrange Polynomial ◽  
Minimum Number ◽  
Mathematical Equations ◽  
Bench Testing ◽  
Engine Type

Abstract The article shows the methodology and calculation procedures based on Lagrange polynomial interpolation which were used to determine standard performance characteristics of the Polish production engine, type ANDORIA 4CTi90-1BE6. They allow to simplify the experimental research by maintaining a minimum number of measurement points and estimating the remaining data in an analytical way. The methods presented are convenient when it comes to the practical side because they eliminate the need for exploration of mathematical equations describing the various curves, which can be cumbersome and time consuming in the case of nonautomated accounts. The results of analysis were applied to actual experimental results, indicating sufficient accuracy of the resulting approximations. As a result, procedures may be used in bench testing of a similar profile, especially with repeated cycles of the experiment, such as optimization of operating parameters of combustion engines.

scholarly journals Morphological Precision Assessment of Reconstructed Surface Models for a Coral Atoll Lagoon

2018 ◽  
Vol 10 (8) ◽  
pp. 2749
Author(s):  
Qi Wang ◽  
Fenzhen Su ◽  
Yu Zhang ◽  
Huiping Jiang ◽  
Fei Cheng
Keyword(s):  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Effective Means ◽  
Slope Aspect ◽  
Change Rate ◽  
Local Slope ◽  
Evaluation Approach ◽  
Multiple Precision ◽  
Surface Models ◽  
Reconstructed Surface

In addition to remote-sensing monitoring, reconstructing morphologic surface models through interpolation is an effective means to reflect the geomorphological evolution, especially for the lagoons of coral atolls, which are underwater. However, which interpolation method is optimal for lagoon geomorphological reconstruction and how to assess the morphological precision have been unclear. To address the aforementioned problems, this study proposed a morphological precision index system including the root mean square error (RMSE) of the elevation, the change rate of the local slope shape (CRLSS), and the change rate of the local slope aspect (CRLSA), and introduced the spatial appraisal and valuation approach of environment and ecosystems (SAVEE). In detail, ordinary kriging (OK), inverse distance weighting (IDW), radial basis function (RBF), and local polynomial interpolation (LPI) were used to reconstruct the lagoon surface models of a typical coral atoll in South China Sea and the morphological precision of them were assessed, respectively. The results are as follows: (i) OK, IDW, and RBF exhibit the best performance in terms of RMSE (0.3584 m), CRLSS (51.43%), and CRLSA (43.29%), respectively, while with insufficiently robust when considering all three aspects; (ii) IDW, LPI, and RBF are suitable for lagoon slopes, lagoon bottoms, and patch reefs, respectively; (iii) The geomorphic decomposition scale is an important factor that affects the precision of geomorphologic reconstructions; and, (iv) This system and evaluation approach can more comprehensively consider the differences in multiple precision indices.

scholarly journals Semi-Infinite Structure Analysis with Bimodular Materials with Infinite Element

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 641
Author(s):  
Wang Huang ◽  
Jianjun Yang ◽  
Jan Sladek ◽  
Vladimir Sladek ◽  
Pihua Wen
Keyword(s):  
Finite Element Method ◽  
Numerical Solutions ◽  
Shape Function ◽  
Polynomial Interpolation ◽  
Finite Domain ◽  
Mapping Technique ◽  
Lagrange Polynomial ◽  
Block Method ◽  
Nonlinear Characteristics ◽  
Typical Material

The modulus of elasticity of some materials changes under tensile and compressive states is simulated by constructing a typical material nonlinearity in a numerical analysis in this paper. The meshless Finite Block Method (FBM) has been developed to deal with 3D semi-infinite structures in the bimodular materials in this paper. The Lagrange polynomial interpolation is utilized to construct the meshless shape function with the mapping technique to transform the irregular finite domain or semi-infinite physical solids into a normalized domain. A shear modulus strategy is developed to present the nonlinear characteristics of bimodular material. In order to verify the efficiency and accuracy of FBM, the numerical results are compared with both analytical and numerical solutions provided by Finite Element Method (FEM) in four examples.

scholarly journals Comparative study of the implementation of the Lagrange interpolation algorithm on GPU and CPU using CUDA to compute the density of a material at different temperatures

2021 ◽  
Vol 119 ◽  
pp. 07002
Author(s):  
Youness Rtal ◽  
Abdelkader Hadjoudja
Keyword(s):  
Parallel Computing ◽  
Graphics Processing Units ◽  
Lagrange Interpolation ◽  
Polynomial Interpolation ◽  
Programming Model ◽  
Interpolation Method ◽  
Processing Unit ◽  
Central Processing ◽  
Computational Performance ◽  
Different Temperatures

Graphics Processing Units (GPUs) are microprocessors attached to graphics cards, which are dedicated to the operation of displaying and manipulating graphics data. Currently, such graphics cards (GPUs) occupy all modern graphics cards. In a few years, these microprocessors have become potent tools for massively parallel computing. Such processors are practical instruments that serve in developing several fields like image processing, video and audio encoding and decoding, the resolution of a physical system with one or more unknowns. Their advantages: faster processing and consumption of less energy than the power of the central processing unit (CPU). In this paper, we will define and implement the Lagrange polynomial interpolation method on GPU and CPU to calculate the sodium density at different temperatures Ti using the NVIDIA CUDA C parallel programming model. It can increase computational performance by harnessing the power of the GPU. The objective of this study is to compare the performance of the implementation of the Lagrange interpolation method on CPU and GPU processors and to deduce the efficiency of the use of GPUs for parallel computing.

scholarly journals Improvement of LTE Downlink System Performances Using the Lagrange Polynomial Interpolation

2014 ◽  
Vol 6 (5) ◽  
pp. 129-143
Author(s):  
Mallouki Nasreddine ◽  
Nsiri Bechir ◽  
Walid Hakimi ◽  
Mahmoud Ammar
Keyword(s):  
Polynomial Interpolation ◽  
Lagrange Polynomial ◽  
Downlink System

Threshold value estimation of journey-distance using generalized polynomial function

2021 ◽  
pp. 1-17
Author(s):  
Roy Subhojit
Keyword(s):  
Polynomial Function ◽  
Polynomial Interpolation ◽  
Interpolation Method ◽  
A Priori ◽  
Threshold Value ◽  
Rate Of Change ◽  
Cumulative Frequency Distribution ◽  
Generalized Polynomial ◽  
Value Estimation ◽  
Mode A

The present work demonstrates an experience in estimating the threshold value of journey distances travelled by transit passengers using generalized polynomial function. The threshold value of journey distances may be defined as that distance beyond which passengers might no more be interested to travel by their reported mode. A knowledge on this threshold value is realized to be useful to limit the upper-most slab of transit fare, while preparing of a length-based fare matrix table. Theoretically, the threshold value can be obtained at that point on the cumulative frequency distribution (CFD) curve of journey distances at which the maximum rate of change of the slope of curve occurs. In this work, the CFD curve of the journey distance values is empirically modelled using Newton’s Polynomial Interpolation method, which helps to overcome various challenges usually encountered while an assumption of a theoretical probability distribution is considered a priori for the CFD.

PNC in 2D Curve Modeling

2017 ◽  
pp. 87-131
Keyword(s):  
Curve Fitting ◽  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Shape Representation ◽  
Linear Interpolation ◽  
Distribution Functions ◽  
Novel Approach ◽  
Curve Modeling ◽  
Basic Probability ◽  
Pros And Cons

Interpolation methods and curve fitting represent so huge problem that each individual interpolation is exceptional and requires specific solutions. PNC method is such a novel tool with its all pros and cons. The user has to decide which interpolation method is the best in a single situation. The choice is yours if you have any choice. Presented method is such a new possibility for curve fitting and interpolation when specific data (for example handwritten symbol or character) starts up with no rules for polynomial interpolation. This chapter consists of two generalizations: generalization of previous MHR method with various nodes combinations and generalization of linear interpolation with different (no basic) probability distribution functions and nodes combinations. This probabilistic view is novel approach a problem of modeling and interpolation. Computer vision and pattern recognition are interested in appropriate methods of shape representation and curve modeling.

Highly accurate technique for studying some chaotic models described by ABC-fractional differential equations of variable-order

2020 ◽  
pp. 2150018
Author(s):  
M. M. Khader ◽  
Ibrahim Al-Dayel
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Polynomial Interpolation ◽  
Numerical Technique ◽  
Variable Order ◽  
Lagrange Polynomial ◽  
Efficient Tool ◽  
Fractional Differential ◽  
The Given

The propose of this paper is to introduce and investigate a highly accurate technique for solving the fractional Logistic and Ricatti differential equations of variable-order. We consider these models with the most common nonsingular Atangana–Baleanu–Caputo (ABC) fractional derivative which depends on the Mittag–Leffler kernel. The proposed numerical technique is based upon the fundamental theorem of the fractional calculus as well as the Lagrange polynomial interpolation. We satisfy the efficiency and the accuracy of the given procedure; and study the effect of the variation of the fractional-order [Formula: see text] on the behavior of the solutions due to the presence of ABC-operator by evaluating the solution with different values of [Formula: see text]. The results show that the given procedure is an easy and efficient tool to investigate the solution for such models. We compare the numerical solutions with the exact solution, thereby showing excellent agreement which we have found by applying the ABC-derivatives. We observe the chaotic solutions with some fractional-variable-order functions.

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