3rd and 11th orders of accuracy of ‘linear’ and ‘quadratic’ elements for Poisson equation with irregular interfaces on Cartesian meshes

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Alexander Idesman ◽  
Bikash Dey
Keyword(s):  
Finite Elements ◽  
Truncation Error ◽  
Complex Geometry ◽  
Computation Time ◽  
Numerical Techniques ◽  
Order Of Accuracy ◽  
Content Type ◽  
Cartesian Meshes ◽  
Increase In Accuracy ◽  
Mesh Generators

Purpose The purpose of this paper is as follows: to significantly reduce the computation time (by a factor of 1,000 and more) compared to known numerical techniques for real-world problems with complex interfaces; and to simplify the solution by using trivial unfitted Cartesian meshes (no need in complicated mesh generators for complex geometry). Design/methodology/approach This study extends the recently developed optimal local truncation error method (OLTEM) for the Poisson equation with constant coefficients to a much more general case of discontinuous coefficients that can be applied to domains with different material properties (e.g. different inclusions, multi-material structural components, etc.). This study develops OLTEM using compact 9-point and 25-point stencils that are similar to those for linear and quadratic finite elements. In contrast to finite elements and other known numerical techniques for interface problems with conformed and unfitted meshes, OLTEM with 9-point and 25-point stencils and unfitted Cartesian meshes provides the 3-rd and 11-th order of accuracy for irregular interfaces, respectively; i.e. a huge increase in accuracy by eight orders for the new 'quadratic' elements compared to known techniques at similar computational costs. There are no unknowns on interfaces between different materials; the structure of the global discrete system is the same for homogeneous and heterogeneous materials (the difference in the values of the stencil coefficients). The calculation of the unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of OLTEM at a given stencil width. The numerical results with irregular interfaces show that at the same number of degrees of freedom, OLTEM with the 9-points stencils is even more accurate than the 4-th order finite elements; OLTEM with the 25-points stencils is much more accurate than the 7-th order finite elements with much wider stencils and conformed meshes. Findings The significant increase in accuracy for OLTEM by one order for 'linear' elements and by 8 orders for 'quadratic' elements compared to that for known techniques. This will lead to a huge reduction in the computation time for the problems with complex irregular interfaces. The use of trivial unfitted Cartesian meshes significantly simplifies the solution and reduces the time for the data preparation (no need in complicated mesh generators for complex geometry). Originality/value It has been never seen in the literature such a huge increase in accuracy for the proposed technique compared to existing methods. Due to a high accuracy, the proposed technique will allow the direct solution of multiscale problems without the scale separation.

Model of induction brazing of nonmagnetic metals using model order reduction approach

2018 ◽  
Vol 37 (4) ◽  
pp. 1515-1524 ◽  
Author(s):  
Pavel Karban ◽  
David Pánek ◽  
Ivo Doležel
Keyword(s):  
Heat Treatment ◽  
Model Order Reduction ◽  
Computation Time ◽  
Order Reduction ◽  
Nonlinear Problems ◽  
Model Order ◽  
Content Type ◽  
Weakly Nonlinear ◽  
Induction Brazing ◽  
Multiphysics Problems

Purpose A novel technique for control of complex physical processes based on the solution of their sufficiently accurate models is presented. The technique works with the model order reduction (MOR), which significantly accelerates the solution at a still acceptable uncertainty. Its advantages are illustrated with an example of induction brazing. Design/methodology/approach The complete mathematical model of the above heat treatment process is presented. Considering all relevant nonlinearities, the numerical model is reduced using the orthogonal decomposition and solved by the finite element method (FEM). It is cheap compared with classical FEM. Findings The proposed technique is applicable in a wide variety of linear and weakly nonlinear problems and exhibits a good degree of robustness and reliability. Research limitations/implications The quality of obtained results strongly depends on the temperature dependencies of material properties and degree of nonlinearities involved. In case of multiphysics problems characterized by low nonlinearities, the results of solved problems differ only negligibly from those solved on the full model, but the computation time is lower by two and more orders. Yet, however, application of the technique in problems with stronger nonlinearities was not fully evaluated. Practical implications The presented model and methodology of its solution may represent a basis for design of complex technologies connected with induction-based heat treatment of metal materials. Originality/value Proposal of a sophisticated methodology for solution of complex multiphysics problems established the MOR technology that significantly accelerates their solution at still acceptable errors.

Secured data aggregation in wireless sensor networks

Sensor Review ◽  
2018 ◽  
Vol 38 (3) ◽  
pp. 369-375 ◽  
Author(s):  
Sathya D. ◽  
Ganesh Kumar P.
Keyword(s):  
Wireless Sensor Networks ◽  
Energy Consumption ◽  
Sensor Networks ◽  
Data Aggregation ◽  
Computation Time ◽  
Wireless Sensor ◽  
Content Type ◽  
Homomorphic Cryptosystem ◽  
Secured Data ◽  
Time And Energy

PurposeThis study aims to provide a secured data aggregation with reduced energy consumption in WSN. Data aggregation is the process of reducing communication overhead in wireless sensor networks (WSNs). Presently, securing data aggregation is an important research issue in WSNs due to two facts: sensor nodes deployed in the sensitive and open environment are easily targeted by adversaries, and the leakage of aggregated data causes damage in the networks, and these data cannot be retrieved in a short span of time. Most of the traditional cryptographic algorithms provide security for data aggregation, but they do not reduce energy consumption.Design/methodology/approachNowadays, the homomorphic cryptosystem is used widely to provide security with low energy consumption, as the aggregation is performed on the ciphertext without decryption at the cluster head. In the present paper, the Paillier additive homomorphic cryptosystem and Bonehet al.’s aggregate signature method are used to encrypt and to verify aggregate data at the base station.FindingsThe combination of the two algorithms reduces computation time and energy consumption when compared with the state-of-the-art techniques.Practical implicationsThe secured data aggregation is useful in health-related applications, military applications, etc.Originality/valueThe new combination of encryption and signature methods provides confidentiality and integrity. In addition, it consumes less computation time and energy consumption than existing methods.

Investigation of magnet segmentation techniques for eddy current losses reduction in permanent magnets electrical machines

2015 ◽  
Vol 34 (1) ◽  
pp. 46-60 ◽  
Author(s):  
Belli Zoubida ◽  
Mohamed Rachid Mekideche
Keyword(s):  
Genetic Algorithm ◽  
Finite Elements ◽  
Eddy Current ◽  
Permanent Magnets ◽  
Skin Effect ◽  
Electrical Machines ◽  
Design Parameters ◽  
Finite Elements Analysis ◽  
Eddy Current Losses ◽  
Content Type

Purpose – Reducing eddy current losses in magnets of electrical machines can be obtained by means of several techniques. The magnet segmentation is the most popular one. It imposes the least restrictions on machine performances. This paper investigates the effectiveness of the magnet circumferential segmentation technique to reduce these undesirable losses. The full and partial magnet segmentation are both studied for a frequency range from few Hz to a dozen of kHz. To increase the efficiency of these techniques to reduce losses for any working frequency, an optimization strategy based on coupling of finite elements analysis and genetic algorithm is applied. The purpose of this paper is to define the parameters of the total and partial segmentation that can ensure the best reduction of eddy current losses. Design/methodology/approach – First, a model to analyze eddy current losses is presented. Second, the effectiveness of full and partial magnet circumferential segmentation to reduce eddy loss is studied for a range of frequencies from few Hz to a dozen of kHz. To achieve these purposes a 2-D finite element model is developed under MATLAB environment. In a third step of the work, an optimization process is applied to adjust the segmentation design parameters for best reduction of eddy current losses in case of surface mounted permanent magnets synchronous machine. Findings – In case of the skin effect operating, both full and partial magnet segmentations can lead to eddy current losses increases. Such deviations of magnet segmentation techniques can be avoided by an appropriate choice of their design parameters. Originality/value – Few works are dedicated to investigate partial magnet segmentation for eddy current losses reduction. This paper studied the effectiveness and behaviour of partial segmentation for different frequency ranges. To avoid eventual anomalies related to the skin effect an optimization process based on the association of the finite elements analysis to genetic algorithm method is adopted.

scholarly journals GEOMETRY MODELING OF 3D TURBINE STAGES - HOW TO OBTAIN HIGH QUALITY GRID AND OVERCOME DISCRETIZATION PROBLEMS

2016 ◽  
Vol 4 (2) ◽  
pp. 197-205
Author(s):  
Galina Ilieva
Keyword(s):  
Finite Elements ◽  
Complex Geometry ◽  
Turbine Blades ◽  
Grid Generation ◽  
Current Paper ◽  
High Quality ◽  
Compressor Blades ◽  
Geometry Modeling ◽  
Wide Range ◽  
Flow Domain

The process of geometry modeling of 3D turbine blades is basically related to the necessity of finite elements with high quality to be obtained, in the process of flow domain approximation. Various approaches for geometry modeling and grid generation, ways to attain elements of high quality and having positive volumes, have been under research and are presented in current paper. Developed methodology and established techniques to high quality grid, are implemented into practice, for geometry modeling of a wide range of turbine and compressor blades of complex geometry.

Parallel calibration based on modified trim strategy

2019 ◽  
Vol 40 (2) ◽  
pp. 249-256
Author(s):  
Yaxin Peng ◽  
Naiwu Wen ◽  
Chaomin Shen ◽  
Xiaohuang Zhu ◽  
Shihui Ying
Keyword(s):  
Computation Time ◽  
Extraction Methods ◽  
Intelligent Manufacturing ◽  
Feature Descriptor ◽  
Data Sets ◽  
Rigid Transformation ◽  
Robot Calibration ◽  
Content Type ◽  
Partial Alignment ◽  
Point Set

Purpose Partial alignment for 3 D point sets is a challenging problem for laser calibration and robot calibration due to the unbalance of data sets, especially when the overlap of data sets is low. Geometric features can promote the accuracy of alignment. However, the corresponding feature extraction methods are time consuming. The purpose of this paper is to find a framework for partial alignment by an adaptive trimmed strategy. Design/methodology/approach First, the authors propose an adaptive trimmed strategy based on point feature histograms (PFH) coding. Second, they obtain an initial transformation based on this partition, which improves the accuracy of the normal direction weighted trimmed iterative closest point (ICP) method. Third, they conduct a series of GPU parallel implementations for time efficiency. Findings The initial partition based on PFH feature improves the accuracy of the partial registration significantly. Moreover, the parallel GPU algorithms accelerate the alignment process. Research limitations/implications This study is applicable to rigid transformation so far. It could be extended to non-rigid transformation. Practical implications In practice, point set alignment for calibration is a technique widely used in the fields of aircraft assembly, industry examination, simultaneous localization and mapping and surgery navigation. Social implications Point set calibration is a building block in the field of intelligent manufacturing. Originality/value The contributions are as follows: first, the authors introduce a novel coarse alignment as an initial calibration by PFH descriptor similarity, which can be viewed as a coarse trimmed process by partitioning the data to the almost overlap part and the rest part; second, they reduce the computation time by GPU parallel coding during the acquisition of feature descriptor; finally, they use the weighted trimmed ICP method to refine the transformation.

Electrocardiogram stream level correlated patterns as features to classify heartbeats for arrhythmia prediction

2020 ◽  
Vol 54 (5) ◽  
pp. 685-701
Author(s):  
Fuad Ali Mohammed Al-Yarimi ◽  
Nabil Mohammed Ali Munassar ◽  
Fahd N. Al-Wesabi
Keyword(s):  
Supervised Learning ◽  
Computation Time ◽  
Classification Error ◽  
Clinical Practices ◽  
Content Type ◽  
A Value ◽  
Correlated Patterns ◽  
Constructive Models ◽  
Minimum Classification Error ◽  
Supervised Learning And Classification

PurposeDigital computing and machine learning-driven predictive analysis in the diagnosis of non-communicable diseases are gaining significance. Globally many research studies are focusing on developing comprehensive models for such detection. Categorically in the proposed diagnosis for arrhythmia, which is a critical diagnosis to prevent cardiac-related deaths, any constructive models can be a value proposition. In this study, the focus is on developing a holistic system that predicts the scope of arrhythmia from the given electrocardiogram report. The proposed method is using the sequential patterns of the electrocardiogram elements as features.Design/methodology/approachConsidering the decision accuracy of the contemporary classification methods, which is not adequate to use in clinical practices, this manuscript coined a new dimension of features to perform supervised learning and classification using the AdaBoost classifier. The proposed method has titled “Electrocardiogram stream level correlated patterns as features (ESCPFs),” which takes electrocardiograms (ECGs) signal streams as input records to perform supervised learning-based classification to detect the arrhythmia scope in given ECG record.FindingsFrom the results and comparative reports generated for the study, it is evident that the model is performing with higher accuracy compared to some of the earlier models. However, focusing on the emerging solutions and technologies, if the accuracy factors for the model can be improved, it can lead to compelling predictions and accurate outcome from the process.Originality/valueThe authors represent complete automatic and rapid arrhythmia as classifier, which could be applied online and examine long ECG records sequence efficiently. By releasing the needs for extraction of features, the authors project an application based on raw signals, one result to heart rates date, whose objective is to lessen computation time when attaining minimum classification error outcomes.

scholarly journals Impact of vapor polishing on surface quality and mechanical properties of extruded ABS

2018 ◽  
Vol 24 (2) ◽  
pp. 501-508 ◽  
Author(s):  
Clayton Neff ◽  
Matthew Trapuzzano ◽  
Nathan B. Crane
Keyword(s):  
Mechanical Properties ◽  
Surface Roughness ◽  
Surface Quality ◽  
Complex Geometry ◽  
Substantial Impact ◽  
Solvent Vapor ◽  
Content Type ◽  
Minimal Impact ◽  
End Use ◽  
Traditional Manufacturing

Purpose Additive manufacturing (AM) is readily capable of producing models and prototypes of complex geometry and is advancing in creating functional parts. However, AM processes typically underperform traditional manufacturing methods in mechanical properties, surface roughness and hermeticity. Solvent vapor treatments (vapor polishing) are commonly used to improve surface quality in thermoplastic parts, but the results are poorly characterized. Design/methodology/approach This work quantifies the surface roughness change and also evaluates the effect on hermeticity and mechanical property impacts for “as-printed” and acetone vapor-polished ABS tensile specimens of 1-, 2- and 4-mm thicknesses produced by material extrusion (FDM). Findings Vapor polishing proves to decrease the power spectral density for surface roughness features larger than 20 µm by a factor of 10× and shows significant improvement in hermeticity based on both perfluorocarbon gross leak and pressure leak tests. However, there is minimal impact on mechanical properties with the thin specimens showing a slight increase in elongation at break but decreased elastic modulus. A bi-exponential diffusion decay model for solvent evaporation suggest a thickness-independent and thickness-dependent time constant with the latter supporting a plasticizing effect on mechanical properties. Originality/value The contributions of this work show vapor polishing can have a substantial impact on the performance for end-use application of ABS FDM components.

Harmonic form-finding for the design of doubly-curved shells

2019 ◽  
Vol 37 (3) ◽  
pp. 1073-1091
Author(s):  
Cecilie Brandt-Olsen ◽  
Paul Shepherd ◽  
Paul Richens
Keyword(s):  
Complex Geometry ◽  
British Museum ◽  
Degree Of Freedom ◽  
Free Form ◽  
Single Degree Of Freedom ◽  
Content Type ◽  
Boundary Constraints ◽  
Single Degree ◽  
Spatial Configurations ◽  
Doubly Curved

Purpose Shell structures are highly efficient and are an elegant way of covering large uninterrupted spaces, but their complex geometry is notoriously difficult to model and analyse. This paper aims to describe a novel free-form shell modelling technique based on structural harmonics. Design/methodology/approach The method builds on work using weighted eigenmodes for three-dimensional mesh modelling in a computer graphics setting and extends it by specifically adapting the technique to an architectural design context. This not only enables the sculpting of free-form architectural surfaces using only a few control parameters but also takes advantage of the synergies between eigenmodes and structural buckling modes, to provide an efficient means of stiffening a shell against failure by buckling. Findings The result is a flexible free-form modelling tool that not only enables the creation of arbitrary doubly curved surfaces but also allows simultan. The tool helps to assist in the design of shells at the conceptual stage and encourages an interaction between the architect and engineer. A number of initiatives, including a single degree of freedom design, boundary constraints, visualisation aids and guidelines towards specific spatial configurations have been introduced to satisfactorily adapt the method to an architectural context. Originality/value The tool helps to assist in the design of shells at the conceptual stage and encourages an interaction between the architect and engineer. A number of initiatives, including a single degree of freedom design, boundary constraints, visualisation aids and guidelines towards specific spatial configurations have been introduced to satisfactorily adapt the method to an architectural context. This paper includes a full case study of the iconic British Museum Great Court Roof to demonstrate the applicability of the developed framework to real-world problems and the software developed to implement the method is available as an open-source download.

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