Anderson acceleration for electromagnetic nonlinear problems

2019 ◽  
Vol 38 (5) ◽  
pp. 1493-1506
Author(s):  
Mattia Filippini ◽  
Piergiorgio Alotto ◽  
Alessandro Giust
Keyword(s):  
Finite Element ◽  
Fixed Point ◽  
Nonlinear Problems ◽  
Test Case ◽  
Test Cases ◽  
Content Type ◽  
Restarted Gmres ◽  
Acceleration Method ◽  
Anderson Acceleration ◽  
Element Boundary

Purpose The purpose of this paper is to implement the Anderson acceleration for different formulations of eletromagnetic nonlinear problems and analyze the method efficiency and strategies to obtain a fast convergence. Design/methodology/approach The paper is structured as follows: the general class of fixed point nonlinear problems is shown at first, highlighting the requirements for convergence. The acceleration method is then shown with the associated pseudo-code. Finally, the algorithm is tested on different formulations (finite element, finite element/boundary element) and material properties (nonlinear iron, hysteresis models for laminates). The results in terms of convergence and iterations required are compared to the non-accelerated case. Findings The Anderson acceleration provides accelerations up to 75 per cent in the test cases that have been analyzed. For the hysteresis test case, a restart technique is proven to be helpful in analogy to the restarted GMRES technique. Originality/value The acceleration that has been suggested in this paper is rarely adopted for the electromagnetic case (it is normally adopted in the electronic simulation case). The procedure is general and works with different magneto-quasi static formulations as shown in the paper. The obtained accelerations allow to reduce the number of iterations required up to 75 per cent in the benchmark cases. The method is also a good candidate in the hysteresis case, where normally the fixed point schemes are preferred to the Newton ones.

Innovative exploration of safe in-flightcrew escape options

2018 ◽  
Vol 90 (8) ◽  
pp. 1221-1226
Author(s):  
Sreedhar Karunakaran
Keyword(s):  
Wind Tunnels ◽  
Test Case ◽  
Test Cases ◽  
Flight Crew ◽  
External Interference ◽  
Content Type ◽  
Transport Aircraft ◽  
3D Cad ◽  
Computational Fluid Dynamics Cfd ◽  
Actual Trial

Purpose The purpose of this paper is to explore various in-flight crew escape options of a prototype transport aircraft and finalize the option offering safest crew egress for different combinations of contingencies and flight conditions. Design/methodology/approach Various egress options were explored through simulation in a computational fluid dynamics (CFD) software using aircraft 3D CAD model and scalable digital mannequins. For this, certain important contingencies which best describe the extreme aircraft behaviour were identified. Crew escape options, which have least external interference in expected egress trajectory, were selected. Several test simulations representing each feasible combination of contingency, escape option and flight condition were simulated. The option which offers safe crew escape in each test case is deemed to be the safest egress option for the test aircraft. Findings Among five options explored, crew escape through forward ventral hatch provided the safest crew escape for all test cases. The selected option was validated for robustness with additional test cases modelling different anthropometric characteristics of 5th and 50th percentile pilot populations with different postures. Originality/value In-flight validation of safe crew escape option is infeasible by actual trial. Exploration of safe crew options for required number of test cases by any analytical method or by wind tunnels tests is tedious, time consuming and extremely expensive. On the other hand, exploration of safest crew option by CFD, besides being first of its kind, provides convenient option to configure, test and validate different test cases with unmatched benefits in time, cost and simplicity.

An adaptive nonlinear finite element analysis of minimal surface problem based on element energy projection technique

2020 ◽  
Vol 37 (8) ◽  
pp. 2847-2869
Author(s):  
Kaifeng Jiang ◽  
Si Yuan ◽  
Qinyan Xing
Keyword(s):  
Finite Element ◽  
Minimal Surface ◽  
Error Control ◽  
Nonlinear Problems ◽  
Fe Analysis ◽  
Nonlinear Finite Element ◽  
Maximum Norm ◽  
Element Analysis ◽  
Content Type ◽  
Element Energy Projection

Purpose This paper aims to propose a new adaptive strategy for two-dimensional (2D) nonlinear finite element (FE) analysis of the minimal surface problem (MSP) based on the element energy projection (EEP) technique. Design/methodology/approach By linearizing nonlinear problems into a series of linear problems via the Newton method, the EEP technique, which is an effective and reliable point-wise super-convergent displacement recovery strategy for linear FE analysis, can be directly incorporated into the solution procedure. Accordingly, a posteriori error estimate in maximum norm was established and an adaptive 2D nonlinear FE strategy of h-version mesh refinement was developed. Findings Three classical known surfaces, including a singularity problem, were analysed. Moreover, an example whose analytic solution is unavailable was considered and a comparison was made between present results and those computed by the MATLAB PDE toolbox. The results show that the adaptively-generated meshes reflect the difficulties inherent in the problems and the proposed adaptive analysis can produce FE solutions satisfying the user-preset error tolerance in maximum norm with a fair adaptive convergence rate. Originality/value The EEP technique for linear FE analysis was extended to the nonlinear procedure of MSP and can be expected to apply to other 2D nonlinear problems. The employment of the maximum norm makes point-wisely error control on the sought surfaces possible and makes the proposed method distinguished from other adaptive FE analyses.

Enhancing finite element boundary stress predictions for plane and axisymmetric situations

1986 ◽  
Vol 21 (1) ◽  
pp. 33-44 ◽  
Author(s):  
T H Richards ◽  
M J Daniels
Keyword(s):  
Finite Element ◽  
Test Cases ◽  
Boundary Stress ◽  
Element Boundary ◽  
Finite Element Stress

The formulation and implementation of a procedure for enhancing finite element stress predictions is described. The efficiency of the process is demonstrated by application to test cases.

8-node and 12-node plane elements based on assumed stress quasi-conforming method immune to distorted mesh

2017 ◽  
Vol 34 (8) ◽  
pp. 2731-2751 ◽  
Author(s):  
Changsheng Wang ◽  
Yang Wang ◽  
Caixia Yang ◽  
Xiangkui Zhang ◽  
Ping Hu
Keyword(s):  
Finite Element ◽  
Analytical Solutions ◽  
Element Mesh ◽  
Content Type ◽  
Mesh Model ◽  
Distorted Mesh ◽  
New Strategy ◽  
Discrete Methods ◽  
Element Boundary ◽  
Fundamental Analytical Solutions

Purpose Severe accuracy loss may occur when finite element comes to the distorted mesh model, and the calculation may fail when element mesh degenerates into concave quadrangle or the element boundary is curved. This is a valuable research topic, and many efforts have been made to develop new finite element models. This paper aims to propose two quasi-conforming membrane elements based on the assumed stress quasi-conforming method and fundamental analytical solutions to overcome the difficulties. Design/methodology/approach First, the fundamental analytical solutions which satisfied both the equilibrium and the compatibility relations of plane stress problem are used as the initial assumed stress of both elements. Then, the stress-function matrices are used as the weighted functions to weaken the strain-displacement equations, which makes only string-net functions on the boundary of the elements are needed in the process of strain integration. Finally, boundary interpolation functions expressed by unknown nodal displacement parameters are adopted to the process of strain integration. Findings The formulations of both elements are simple and concise, and the elements are immune to the distorted mesh, which can be used to the mesh shape degenerates into a triangle or concave quadrangle and curved-side element. The results of the numerical tests have proven that the new models possess high accuracy. Originality/value New formulations of quasi-conforming method are described is detail, and the new strategy exhibits advantages of both analytical and discrete methods.

scholarly journals Non-invasive implementation of nonlinear isogeometric analysis in an industrial FE software

2019 ◽  
Vol 37 (1) ◽  
pp. 237-261 ◽  
Author(s):  
Marie Tirvaudey ◽  
Robin Bouclier ◽  
Jean-Charles Passieux ◽  
Ludovic Chamoin
Keyword(s):  
Finite Element ◽  
Isogeometric Analysis ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
The Novel ◽  
Input Output ◽  
Element Analysis ◽  
Content Type ◽  
Lagrange Polynomials ◽  
Non Invasive

Purpose The purpose of this paper is to further simplify the use of NURBS in industrial environnements. Although isogeometric analysis (IGA) has been the object of intensive studies over the past decade, its massive deployment in industrial analysis still appears quite marginal. This is partly due to its implementation, which is not straightforward with respect to the elementary structure of finite element (FE) codes. This often discourages industrial engineers from adopting isogeometric capabilities in their well-established simulation environment. Design/methodology/approach Based on the concept of Bézier and Lagrange extractions, a novel method is proposed to implement IGA from an existing industrial FE code with the aim of bringing human implementation effort to the minimal possible level (only using standard input-output of finite element analysis (FEA) codes, avoid code-dependent subroutines implementation). An approximate global link to go from Lagrange polynomials to non-uniform-rational-B-splines functions is formulated, which enables the whole FE routines to be untouched during the implementation. Findings As a result, only the linear system resolution step is bypassed: the resolution is performed in an external script after projecting the FE system onto the reduced, more regular and isogeometric basis. The novel procedure is successfully validated through different numerical experiments involving linear and nonlinear isogeometric analyses using the standard input/output of the industrial FE software Code_Aster. Originality/value A non-invasive implementation of IGA into FEA software is proposed. The whole FE routines are untouched during the novel implementation procedure; a focus is made on the IGA solution of nonlinear problems from existing FEA software; technical details on the approach are provided by means of illustrative examples and step-by-step implementation; the methodology is evaluated on a range of two- and three-dimensional elasticity and elastoplasticity benchmarks solved using the commercial software Code_Aster.

Numerical implementation of finite-element method of control volume using irregular mesh

2010 ◽  
Vol 7 ◽  
pp. 98-108
Author(s):  
Yu.A. Gafarova
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Delaunay Triangulation ◽  
Complex Geometry ◽  
Control Volume ◽  
Test Case ◽  
The Finite Element Method ◽  
Irregular Mesh ◽  
Discrete Analogues ◽  
Element Method

To solve problems with complex geometry it is considered the possibility of application of irregular mesh and the use of various numerical methods using them. Discrete analogues of the Beltrami-Mitchell equations are obtained by the control volume method using the rectangular grid and the finite element method of control volume using the Delaunay triangulation. The efficiency of using the Delaunay triangulation, Voronoi diagrams and the finite element method of control volume in a test case is demonstrated.

scholarly journals Resource and dependency based test case generation for RESTful Web services

2021 ◽  
Vol 26 (4) ◽  
Author(s):  
Man Zhang ◽  
Bogdan Marculescu ◽  
Andrea Arcuri
Keyword(s):  
Web Services ◽  
Domain Knowledge ◽  
Automated System ◽  
Test Case ◽  
Test Cases ◽  
Evolutionary Search ◽  
Sampling Strategies ◽  
Mutation Operators ◽  
On Line ◽  
Restful Web Services

AbstractNowadays, RESTful web services are widely used for building enterprise applications. REST is not a protocol, but rather it defines a set of guidelines on how to design APIs to access and manipulate resources using HTTP over a network. In this paper, we propose an enhanced search-based method for automated system test generation for RESTful web services, by exploiting domain knowledge on the handling of HTTP resources. The proposed techniques use domain knowledge specific to RESTful web services and a set of effective templates to structure test actions (i.e., ordered sequences of HTTP calls) within an individual in the evolutionary search. The action templates are developed based on the semantics of HTTP methods and are used to manipulate the web services’ resources. In addition, we propose five novel sampling strategies with four sampling methods (i.e., resource-based sampling) for the test cases that can use one or more of these templates. The strategies are further supported with a set of new, specialized mutation operators (i.e., resource-based mutation) in the evolutionary search that take into account the use of these resources in the generated test cases. Moreover, we propose a novel dependency handling to detect possible dependencies among the resources in the tested applications. The resource-based sampling and mutations are then enhanced by exploiting the information of these detected dependencies. To evaluate our approach, we implemented it as an extension to the EvoMaster tool, and conducted an empirical study with two selected baselines on 7 open-source and 12 synthetic RESTful web services. Results show that our novel resource-based approach with dependency handling obtains a significant improvement in performance over the baselines, e.g., up to + 130.7% relative improvement (growing from + 27.9% to + 64.3%) on line coverage.

scholarly journals Performance of Enhanced Multiple-Searching Genetic Algorithm for Test Case Generation in Software Testing

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1779
Author(s):  
Wanida Khamprapai ◽  
Cheng-Fa Tsai ◽  
Paohsi Wang ◽  
Chi-En Tsai
Keyword(s):  
Genetic Algorithm ◽  
Software Testing ◽  
Random Search ◽  
Automatic Generation ◽  
Superior Performance ◽  
Test Case Generation ◽  
Test Case ◽  
Test Cases ◽  
Network Systems ◽  
Routing Problem

Test case generation is an important process in software testing. However, manual generation of test cases is a time-consuming process. Automation can considerably reduce the time required to create adequate test cases for software testing. Genetic algorithms (GAs) are considered to be effective in this regard. The multiple-searching genetic algorithm (MSGA) uses a modified version of the GA to solve the multicast routing problem in network systems. MSGA can be improved to make it suitable for generating test cases. In this paper, a new algorithm called the enhanced multiple-searching genetic algorithm (EMSGA), which involves a few additional processes for selecting the best chromosomes in the GA process, is proposed. The performance of EMSGA was evaluated through comparison with seven different search-based techniques, including random search. All algorithms were implemented in EvoSuite, which is a tool for automatic generation of test cases. The experimental results showed that EMSGA increased the efficiency of testing when compared with conventional algorithms and could detect more faults. Because of its superior performance compared with that of existing algorithms, EMSGA can enable seamless automation of software testing, thereby facilitating the development of different software packages.

Parallel finite-element method using domain decomposition and Parareal for transient motor starting analysis

2019 ◽  
Vol 38 (5) ◽  
pp. 1507-1520 ◽  
Author(s):  
Yasuhito Takahashi ◽  
Koji Fujiwara ◽  
Takeshi Iwashita ◽  
Hiroshi Nakashima
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parallel Computing ◽  
Domain Decomposition ◽  
Parallel Computation ◽  
Domain Decomposition Method ◽  
Space Time ◽  
Content Type ◽  
Parallel Performance ◽  
Element Method

Purpose This paper aims to propose a parallel-in-space-time finite-element method (FEM) for transient motor starting analyses. Although the domain decomposition method (DDM) is suitable for solving large-scale problems and the parallel-in-time (PinT) integration method such as Parareal and time domain parallel FEM (TDPFEM) is effective for problems with a large number of time steps, their parallel performances get saturated as the number of processes increases. To overcome the difficulty, the hybrid approach in which both the DDM and PinT integration methods are used is investigated in a highly parallel computing environment. Design/methodology/approach First, the parallel performances of the DDM, Parareal and TDPFEM were compared because the scalability of these methods in highly parallel computation has not been deeply discussed. Then, the combination of the DDM and Parareal was investigated as a parallel-in-space-time FEM. The effectiveness of the developed method was demonstrated in transient starting analyses of induction motors. Findings The combination of Parareal with the DDM can improve the parallel performance in the case where the parallel performance of the DDM, TDPFEM or Parareal is saturated in highly parallel computation. In the case where the number of unknowns is large and the number of available processes is limited, the use of DDM is the most effective from the standpoint of computational cost. Originality/value This paper newly develops the parallel-in-space-time FEM and demonstrates its effectiveness in nonlinear magnetoquasistatic field analyses of electric machines. This finding is significantly important because a new direction of parallel computing techniques and great potential for its further development are clarified.

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