scholarly journals A Domain Decomposition Method for Hybrid Shell Vector Element with Boundary Integral Method

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
Lin Lei ◽  
Jun Hu ◽  
Hao-Quan Hu
Keyword(s):  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Three Dimensional ◽  
Shell Element ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Thin Coating ◽  
Surface Integral ◽  
Vector Element ◽  
Element Method

For the conducting body coated with thin-layer material, plenty of fine meshes are required in general. In this paper, shell vector element (SVE) is used for modeling of thin coating dielectric. Further, a domain decomposition (DD) method for hybrid shell vector element method boundary integral (SVE-BI) is proposed for analysis of electromagnetic problem of multiple three-dimensional thin-coating objects. By this method, the whole computational domains are divided into sub-SVE domains and boundary element domains. With shell element, not only the unknowns are far less than the one by traditional vector element method, but only surface integral is required. The DDM framework used for hybrid SVE-BI also enhances the computational efficiency of solving scattering from multiple coating objects greatly. Finally, several numerical examples are presented to prove the accuracy and efficiency of this DDM-SVE-BI method.

A Domain Decomposition of the Finite Element-Boundary Integral Method for Scattering by Deep Cavities

2011 ◽  
Vol 383-390 ◽  
pp. 2585-2589
Author(s):  
Zhi Wei Cui ◽  
Yi Ping Han ◽  
Wen Juan Zhao
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Schur Complement ◽  
Building Blocks ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Special Method ◽  
Deep Cavities ◽  
Element Boundary

An efficient domain decomposition method (DDM) is employed to improve upon the efficiency and capability of the finite element-boundary integral (FE-BI) method for calculation of electromagnetic (EM) scattering from deep cavities. This method first subdivides the original cavity into many sub-domains along its depth and classifies these sub-domains into a few building blocks. It then employs the substructuring method to deal with the different types of sub-domains. The resulting Schur complement system is solved by a special method which has low memory requirements because the formation of the global Schur complement matrix is not necessary. Numerical results indicate that the presented method is an effective approach for scattering by deep cavities.

scholarly journals Solving Scattering from Conducting Body Coated by Thin-Layer Material by Hybrid Shell Vector Element with Boundary Integral Method

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Lin Lei ◽  
Jun Hu ◽  
Hao-Quan Hu
Keyword(s):  
Thin Layer ◽  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Surface Integral ◽  
Coating Materials ◽  
Layer Material ◽  
Tetrahedral Elements ◽  
Conducting Body ◽  
Vector Element

The finite element boundary integral (FEM-BI) method is widely used in the scattering and radiating problems. But for the conducting body coated by thin-layer material, plenty of fine meshes are required to discretize the geometry in the traditional FEM. It requires very expensive storage and CPU time. In this paper, the hybrid shell vector element with the boundary integral method is used to expedite the solution of thin coating problems. The shell vector elements are used to discretize thin-layer material instead of traditional tetrahedral elements. Consequently, the volume integral can be simplified into surface integral. This method reduces the number of unknowns greatly and is also extended into the complicated case of multi-thin-layer coating materials. Several numerical results are presented to prove the accuracy and efficiency of this present 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.

An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Sofia Sarraf ◽  
Ezequiel López ◽  
Laura Battaglia ◽  
Gustavo Ríos Rodríguez ◽  
Jorge D'Elía
Keyword(s):  
Boundary Element Method ◽  
Linear System ◽  
Boundary Element ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Computational Time ◽  
Creeping Flows ◽  
Order Of Magnitude ◽  
Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

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