Numerical integration schemes and parallel computation for wear prediction using finite element method

Wear ◽  
2009 ◽  
Vol 266 (7-8) ◽  
pp. 822-831 ◽  
Author(s):  
Saad Mukras ◽  
Nam H. Kim ◽  
W. Gregory Sawyer ◽  
David B. Jackson ◽  
Lawrence W. Bergquist
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Integration ◽  
Parallel Computation ◽  
Wear Prediction ◽  
Integration Schemes ◽  
Element Method

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.

On the numerical integration in generalized/extended finite element method analysis for crack propagation problems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bruna Caroline Campos ◽  
Felício Bruzzi Barros ◽  
Samuel Silva Penna
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Numerical Integration ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Content Type ◽  
Integration Techniques ◽  
Integration Strategies ◽  
Element Method

Purpose The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered. Design/methodology/approach Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results. Findings Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities. Originality/value This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

Numerical Integration Technique in Computation of Extended Finite Element Method

2012 ◽  
Vol 446-449 ◽  
pp. 3557-3560 ◽  
Author(s):  
Feng Wang ◽  
Di Zhang ◽  
Jing Yu ◽  
Hui Xu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Integration ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Displacement Mode ◽  
Integration Techniques ◽  
Discontinuous Medium ◽  
Control Equation ◽  
Element Method

The extended finite element method (XFEM) is the most effective numerical method to solve discontinuous dynamic problems so far. It makes research within a standard finite element framework and reserves all merits of CFEM. In other side, it needs not mesh repartition to geometric and physical interface. Numerical integration techniques of the XFEM computation are studied, including displacement mode of the XFEM, control equation and infirm solution form of discontinuous medium mechanics problem, region scatteration, element integral strategy.

The Finite-Element Method—Part II

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Integration ◽  
Gaussian Quadrature ◽  
The Finite Element Method ◽  
Gaussian Quadrature Formula ◽  
Stiffness Matrices ◽  
Minimum Number ◽  
Element Technique ◽  
Element Method

Numerical integration is an important part of the finite-element technique. As seen in Section 6.5 of Chap. 6, volume integrations as well as surface integrations should be carried out in order to represent the elemental stiffness equations in a simple matrix form. In deriving the variational principle, it is implicitly assumed that these integrations are exact. However, exact integrations of the terms included in the element matrices are not always possible. In the finite-element method, further approximations are made in the procedure for integration, which is summarized in this section. Numerical integration requires, in general, that the integrand be evaluated at a finite number of points, called Integration points, within the integration limits. The number of integration points can be reduced, while achieving the same degree of accuracy, by determining the locations of integration points selectively. In evaluating integration in the stiffness matrices, it is necessary to use an integration formula that requires the least number of integrand evaluations. Since the Gaussian quadrature is known to require the minimum number of integration points, we use the Gaussian quadrature formula almost exclusively to carry out the numerical integrations.

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