scholarly journals Modelling of a permanent magnet synchronous machine using isogeometric analysis

2018 ◽  
Vol 37 (5) ◽  
pp. 1805-1814 ◽  
Author(s):  
Prithvi Bhat ◽  
Zeger Bontinck ◽  
Jacopo Corno ◽  
Sebastian Schöps ◽  
Herbert DeGersem
Keyword(s):  
Domain Decomposition ◽  
Isogeometric Analysis ◽  
Numerical Solutions ◽  
Permanent Magnet Synchronous Machine ◽  
Computational Domain ◽  
Content Type ◽  
B Splines ◽  
Decomposition Scheme ◽  
Original Contribution ◽  
Good Agreement

Purpose This paper aims to propose the use of isogeometric analysis (IGA) for the simulation of electrical machines to represent their geometries exactly and obtain numerical solutions of high accuracy and regularity. Design/methodology/approach IGA makes use of non-uniform rational b-splines to parametrise the domain and approximate the solution spaces. Dealing with the different stator and rotor topologies, the computational domain is split into two non-overlapping parts on which Maxwell’s equations are solved independently and are interconnected by a classical Schwarz domain decomposition scheme. The results are compared with the conventional polynomial finite element method (FEM). Findings The new methodology is reliable and efficient. The obtained solutions of the fields are in good agreement with the ones obtained by the FEM approach. IGA offers a better accuracy than FEM. Originality/value The application of IGA combined with domain decomposition to the model of an electric machine is a new and original contribution.

Adaptive Numerical Modeling of Engineering Problems Using Hierarchical Fup Basis Functions and Control Volume IsoGeometric Analysis

2021 ◽  
Author(s):  
◽  
Grgo Kamber ◽  
Keyword(s):  
Isogeometric Analysis ◽  
Numerical Solutions ◽  
Control Volume ◽  
Spatial Scales ◽  
Basis Functions ◽  
Approximation Properties ◽  
Unified Framework ◽  
B Splines ◽  
Engineering Problems ◽  
Resolution Level

The main objective of this thesis is to utilize the powerful approximation properties of Fup basis functions for numerical solutions of engineering problems with highly localized steep gradients while controlling spurious numerical oscillations and describing different spatial scales. The concept of isogeometric analysis (IGA) is presented as a unified framework for multiscale representation of the geometry and solution. This fundamentally high-order approach enables the description of all fields as continuous and smooth functions by using a linear combination of spline basis functions. Classical IGA usually employs Galerkin or collocation approach using B-splines or NURBS as basis functions. However, in this thesis, a third concept in the form of control volume isogeometric analysis (CV-IGA) is used with Fup basis functions which represent infinitely smooth splines. Novel hierarchical Fup (HF) basis functions is constructed, enabling a local hp-refinement such that they can replace certain basis functions at one resolution level with new basis functions at the next resolution level that have a smaller length of the compact support (h-refinement), but also higher order (p-refinement). This hp-refinement property enables spectral convergence which is significant improvement in comparison to the hierarchical truncated B-splines which enable h-refinement and polynomial convergence. Thus, in domain zones with larger gradients, the algorithm uses smaller local spatial scales, while in other region, larger spatial scales are used, controlling the numerical error by the prescribed accuracy. The efficiency and accuracy of the adaptive algorithm is verified with some classic 1D and 2D benchmark test cases with application to the engineering problems with highly localized steep gradients and advection-dominated problems.

An enriched formulation of isogeometric analysis applied to the dynamical response of bars and trusses

2020 ◽  
Vol 37 (7) ◽  
pp. 2439-2466
Author(s):  
Mateus Rauen ◽  
Roberto Dalledone Machado ◽  
Marcos Arndt
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Isogeometric Analysis ◽  
Computer Aided Design ◽  
Numerical Solutions ◽  
Dynamical Response ◽  
Generalized Finite Element Method ◽  
Content Type ◽  
High Convergence Rate ◽  
Element Method

Purpose This study aims to present a new hybrid formulation based on non-uniform rational b-splines functions and enrichment strategies applied to free and forced vibration of straight bars and trusses. Design/methodology/approach Based on the idea of enrichment from generalized finite element method (GFEM)/extended finite element method (XFEM), an extended isogeometric formulation (partition of unity isogeometric analysis [PUIGA]) is conceived. By numerical examples the methods are tested and compared with isogeometric analysis, finite element method and GFEM in terms of convergence, error spectrum, conditioning and adaptivity capacity. Findings The results show a high convergence rate and accuracy for PUIGA and the advantage of input enrichment functions and material parameters on parametric space. Originality/value The enrichment strategies demonstrated considerable improvements in numerical solutions. The applications of computer-aided design mapped enrichments applied to structural dynamics are not known in the literature.

A quartic trigonometric tension b-spline algorithm for nonlinear partial differential equation system

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Özlem Ersoy Hepson
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Higher Order ◽  
Spline Collocation ◽  
Partial Differential ◽  
Content Type ◽  
B Spline ◽  
B Splines ◽  
Coupled Burgers Equation

Purpose The purpose of this study is to construct quartic trigonometric tension (QTT) B-spline collocation algorithms for the numerical solutions of the Coupled Burgers’ equation. Design/methodology/approach The finite elements method (FEM) is a numerical method for obtaining an approximate solution of partial differential equations (PDEs). The development of high-speed computers enables to development FEM to solve PDEs on both complex domain and complicated boundary conditions. It also provides higher-order approximation which consists of a vector of coefficients multiplied by a set of basis functions. FEM with the B-splines is efficient due both to giving a smaller system of algebraic equations that has lower computational complexity and providing higher-order continuous approximation depending on using the B-splines of high degree. Findings The result of the test problems indicates the reliability of the method to get solutions to the CBE. QTT B-spline collocation approach has convergence order 3 in space and order 1 in time. So that nonpolynomial splines provide smooth solutions during the run of the program. Originality/value There are few numerical methods build-up using the trigonometric tension spline for solving differential equations. The tension B-spline collocation method is used for finding the solution of Coupled Burgers’ equation.

A Time Second-Order Mass-Conserved Implicit-Explicit Domain Decomposition Scheme for Solving the Diffusion Equations

2017 ◽  
Vol 9 (4) ◽  
pp. 795-817 ◽  
Author(s):  
Zhongguo Zhou ◽  
Dong Liang
Keyword(s):  
Domain Decomposition ◽  
Numerical Solutions ◽  
Domain Decomposition Method ◽  
Stable Condition ◽  
Mass Conservation ◽  
Second Order ◽  
Diffusion Equations ◽  
Time And Space ◽  
Decomposition Scheme ◽  
Correction Step

AbstractIn the paper, a new time second-order mass-conserved implicit/explicit domain decomposition method (DDM) for the diffusion equations is proposed. In the scheme, firstly, we calculate the interface fluxes of sub-domains from the obtained solutions and fluxes at the previous time level, for which we apply high-order Taylor’s expansion and transfer the time derivatives to spatial derivatives to improve the accuracy. Secondly, the interior solutions and fluxes in sub-domains are computed by the implicit scheme and using the relations between solutions and fluxes, without any correction step. The mass conservation is proved and the convergence order of the numerical solutions is proved to be second-order in both time and space steps. The super-convergence of numerical fluxes is also proved to be second-order in both time and space steps. The scheme is stable under the stable conditionr≤3/5. The important feature is that the proposed domain decomposition scheme is mass-conserved and is of second order convergence in time. Numerical experiments confirm the theoretical results.

Model order reducibility of nonlinear electro-quasistatic problems

2019 ◽  
Vol 38 (5) ◽  
pp. 1453-1464
Author(s):  
Fotios Kasolis ◽  
Markus Clemens
Keyword(s):  
Domain Decomposition ◽  
Model Order Reduction ◽  
Design Methodology ◽  
Order Reduction ◽  
Computational Domain ◽  
Computationally Efficient ◽  
Model Order ◽  
Content Type ◽  
Strongly Nonlinear ◽  
Domain Decomposition Algorithm

Purpose This paper aims to develop an automated domain decomposition strategy that is based on the presence of nonlinear field grading material, in the context of model order reduction for transient strongly nonlinear electro-quasistatic (EQS) field problems. Design/methodology/approach The paper provides convincing empirical insights to support the proposed domain decomposition algorithm, a numerical investigation of the performance of the algorithm for different snapshots and model order reduction experiments. Findings The proposed method successfully decomposes the computational domain, while the resulting reduced models are highly accurate. Further, the algorithm is computationally efficient and robust, while it can be embedded in black-box model reduction implementations. Originality/value This paper fulfills the demand to effectively perform model order reduction for transient strongly nonlinear EQS field problems.

Proper orthogonal decomposition Pascal polynomial-based method for solving Sobolev equation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mehdi Dehghan ◽  
Baharak Hooshyarfarzin ◽  
Mostafa Abbaszadeh
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Meshfree Method ◽  
Orthogonal Decomposition ◽  
Sobolev Type ◽  
Computational Domain ◽  
Sobolev Equation ◽  
Content Type ◽  
Proper Orthogonal

Purpose This study aims to use the polynomial approximation method based on the Pascal polynomial basis for obtaining the numerical solutions of partial differential equations. Moreover, this method does not require establishing grids in the computational domain. Design/methodology/approach In this study, the authors present a meshfree method based on Pascal polynomial expansion for the numerical solution of the Sobolev equation. In general, Sobolev-type equations have several applications in physics and mechanical engineering. Findings The authors use the Crank-Nicolson scheme to discrete the time variable and the Pascal polynomial-based (PPB) method for discretizing the spatial variables. But it is clear that increasing the value of the final time or number of time steps, will bear a lot of costs during numerical simulations. An important purpose of this paper is to reduce the execution time for applying the PPB method. To reach this aim, the proper orthogonal decomposition technique has been combined with the PPB method. Originality/value The developed procedure is tested on various examples of one-dimensional, two-dimensional and three-dimensional versions of the governed equation on the rectangular and irregular domains to check its accuracy and validity.

scholarly journals A New Efficient Algorithm for the 2D WLP-FDTD Method Based on Domain Decomposition Technique

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Bo-Ao Xu ◽  
Yan-Tao Duan ◽  
Bin Chen ◽  
Yun Yi ◽  
Kang Luo
Keyword(s):  
Finite Difference ◽  
Domain Decomposition ◽  
Efficient Algorithm ◽  
Laguerre Polynomials ◽  
Fdtd Method ◽  
Computational Domain ◽  
Decomposition Scheme ◽  
Speed Up ◽  
Fdtd Methods ◽  
Difference Time

This letter introduces a new efficient algorithm for the two-dimensional weighted Laguerre polynomials finite difference time-domain (WLP-FDTD) method based on domain decomposition scheme. By using the domain decomposition finite difference technique, the whole computational domain is decomposed into several subdomains. The conventional WLP-FDTD and the efficient WLP-FDTD methods are, respectively, used to eliminate the splitting error and speed up the calculation in different subdomains. A joint calculation scheme is presented to reduce the amount of calculation. Through our work, the iteration is not essential to obtain the accurate results. Numerical example indicates that the efficiency and accuracy are improved compared with the efficient WLP-FDTD method.

Thermal Performance Analysis of a Rectangular Longitudinal Finned Solar Air Heater With Semicircular Absorber Plate

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Satyender Singh ◽  
Prashant Dhiman
Keyword(s):  
Thermal Performance ◽  
Numerical Solutions ◽  
Solar Air Heater ◽  
Duct Flow ◽  
Balance Equations ◽  
Absorber Plate ◽  
Ansys Fluent ◽  
Air Heater ◽  
Glass Cover ◽  
Good Agreement

Thermal performance of a single-pass single-glass cover solar air heater consisting of semicircular absorber plate finned with rectangular longitudinal fins is investigated. The analysis is carried out for different hydraulic diameters, which were obtained by varying the diameter of the duct from 0.3–0.5 m. One to five numbers of fins are considered. Reynolds number ranges from 1600–4300. Analytical solutions for energy balance equations of different elements and duct flow of the solar air heater are presented; results are compared with finite-volume methodology based numerical solutions obtained from ansys fluent commercial software, and a fairly good agreement is achieved. Moreover, analysis is extended to check the effect of double-glass cover and the recycle of the exiting air. Results revealed that the use of double-glass cover and recycle operation improves the thermal performance of solar air heater.

Extended isogeometric analysis using B++ splines for strong discontinuous problems

2021 ◽  
Vol 381 ◽  
pp. 113779
Author(s):  
Wenbin Hou ◽  
Kai Jiang ◽  
Xuefeng Zhu ◽  
Yuanxing Shen ◽  
Ping Hu
Keyword(s):  
Isogeometric Analysis ◽  
B Splines ◽  
Discontinuous Problems

scholarly journals Experimental and Numerical Buckling Analyses of Laminated Composite Plates under Temperature Effects

2010 ◽  
Vol 19 (4) ◽  
pp. 096369351001900 ◽  
Author(s):  
Emin Ergun
Keyword(s):  
Composite Plate ◽  
Numerical Solutions ◽  
Laminated Composite ◽  
Composite Plates ◽  
Buckling Load ◽  
Fibre Reinforcement ◽  
Stacking Sequence ◽  
Laminated Composite Plates ◽  
Different Temperatures ◽  
Good Agreement

The aim of this study is to investigate, experimentally and numerically, the change of critical buckling load in composite plates with different ply numbers, orientation angles, stacking sequences and boundary conditions as a function of temperature. Buckling specimens have been removed from the composite plate with glass-fibre reinforcement at [0°]i and [45°]i (i= number of ply). First, the mechanical properties of the composite material were determined at different temperatures, and after that, buckling experiments were done for those temperatures. Then, numerical solutions were obtained by modelling the specimens used in the experiment in the Ansys10 finite elements package software. The experimental and numerical results are in very good agreement with each other. It was found that the values of the buckling load at [0°] on the composite plates are higher than those of other angles. Besides, symmetrical and anti-symmetrical conditions were examined to see the effect of the stacking sequence on buckling and only numerical solutions were obtained. It is seen that the buckling load reaches the highest value when it is symmetrical in the cross-ply stacking sequence and it is anti-symmetrical in the angle-ply stacking sequence.

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