Voxel Based Finite Element Method Using Homogenization

Watanabe, Kazuhiro; Iijima, Yosuke; Kawano, Kenji; Igarashi, Hajime

doi:10.1109/tmag.2011.2176322

Cited by 14 publications

(5 citation statements)

References 13 publications

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“…In order to further improve the computational accuracy, the homogenization technique is introduced. Although homogenization techniques have usually been employed to compute effective material constant of inhomogeneous materials and laminated iron cores in FEM, they have been employed in few studies to compute effective reluctivity of voxels at the material boundaries (Watanabe et al, 2012). Using the simple homogenization method, the effective reluctivity of boundary elements, v h , is computed as follows:…”

Section: Homogenizationmentioning

confidence: 99%

Accuracy evaluation of three-dimensional FE analysis based on nonconforming voxel element

Satô

Watanabe

Igarashi

2013

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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Purpose -Three-dimensional (3D) mesh generation for shape optimizations needs long computational time. This makes it difficult to perform 3D shape optimizations. The purpose of this paper is to present a new meshing method with light computational cost for 3D shape optimizations. Design/methodology/approach -This paper presents a new meshing method on the basis of nonconforming voxel finite element method. The 3D mesh generation is performed with light computational cost keeping the computational accuracy. Findings -It is shown that the computational cost for 3D mesh generation can be reduced without deteriorating numerical accuracy in the FE analysis. It is reported the performance of the present method. Originality/value -The validity of the nonconforming voxel elements is tested to apply it to the optimization of 3D optimizations.

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Section: Homogenizationmentioning

confidence: 99%

Accuracy evaluation of three-dimensional FE analysis based on nonconforming voxel element

Satô

Watanabe

Igarashi

2013

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering

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“…Efforts have been made to analyze or improve the accuracy of unfitted FE analysis [1]- [4]. An effective approach adopted in several recent papers [2], [3] is to incorporate (or replace some of the standard FE shape functions by) special shape functions that represent the exceptional behavior of the fields in the unfitted elements.…”

Section: Introductionmentioning

confidence: 99%

“…Reference [4] presented homogenization as an alternative approach. In the homogenization approach, one determines the homogenized material properties, which are elementwise constant, of the unfitted elements so as to improve the accuracy of the whole analysis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Interface Homogenization Technique for Unfitted Finite Element Electromagnetic Analysis

Mifune

2015

IEEE Trans. Magn.

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In some finite-element applications, the use of an unfitted mesh can mitigate the complexity of tasks involving mesh generation, although the lack of fit of the mesh and material interface may cause a large numerical error around the interface. This paper presents a new homogenization technique that reduces the error caused by the lack of fit. The proposed technique determines the material properties of the unfitted elements, so as to guarantee that numerical solutions coincide with the analytical solution, in the simplest situation, where the field is uniform in each of the two materials around a flat interface. Numerical tests demonstrate the effectiveness of the new technique.Index Terms-Anisotropy, finite-element (FE) method, moving interface, unfitted mesh.

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“…T HE nonconforming voxel finite-element method (NVFEM) uses a nested grid of rectangular elements [1]- [3]. Unlike the conventional finite-element (FE) method, the elements do not fit the geometry exactly, but only in a staircase manner.…”

Section: Introductionmentioning

confidence: 99%

Computed Basis Functions for 2-D Edge Elements

Nazari

Webb

2015

IEEE Trans. Magn.

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The nonconforming voxel finite-element method (NVFEM) models material boundaries in a staircase fashion. Recently, a technique called the computed basis function (CBF) method was introduced to reduce the errors arising from this, but it was applied only to scalar fields. Here, the CBF method is developed for vector fields that are represented with 2-D edge elements. The method is tested by solving the vector wave equation for problems involving perfectly conducting or dielectric obstacles. Results show that NVFEM enhanced with CBF can achieve the same accuracy as NVFEM with between 6 and 10 times fewer unknowns, with no reduction in the sparsity of the global FE matrix.

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Voxel Based Finite Element Method Using Homogenization

Cited by 14 publications

References 13 publications

Accuracy evaluation of three-dimensional FE analysis based on nonconforming voxel element

Accuracy evaluation of three-dimensional FE analysis based on nonconforming voxel element

Interface Homogenization Technique for Unfitted Finite Element Electromagnetic Analysis

Computed Basis Functions for 2-D Edge Elements

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