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A massively parallel matrix free finite element based multigrid method for simulations of heterogeneous materials using tomographic images

Abstract : Numerical simulations using X-ray based Computed Tomography (CT) images became more and more common in the last two decades. CT images give researchers ample information about material microstructures. Performing numerical simulation at the microscopical scale permits researchers to understand the thermal and mechanical behavior of materials, and to improve material performance. The difficulties of performing simulations come from the complexity and the dimension of images. The meshing generation for the complex microstructure requires human intervention when using the finite element method. Simulations using large scale CT images are memory and time consuming. The objective is to overcome these difficulties and to perform automatically numerical simulations directly from CT images. The matrix free finite element method (MF-FEM) is applied to diminish the memory requirements. A MultiGrid (MG) method is used to improve the convergence of the MF-FEM. An efficient homogenization method to compute the coarse grid operator of MG methods is proposed to insure the convergence of MG methods for problems with large material property variations. Massively parallel computing is applied to deal with time consumption problem. Numerical simulations directly from CT images with billions of degrees of freedom are finally performed on the thermal and mechanical problems.
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Submitted on : Thursday, February 27, 2020 - 4:08:15 PM
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Xiaodong Liu. A massively parallel matrix free finite element based multigrid method for simulations of heterogeneous materials using tomographic images. Mechanics of materials [physics.class-ph]. École centrale de Nantes, 2019. English. ⟨NNT : 2019ECDN0057⟩. ⟨tel-02493207⟩

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