Local Homogenization and Computations

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Local Homogenization and Computations
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Outline
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Local Homogenization
Homogenization for a specific coarse mesh
Define a coarse mesh
Assembled homogenized Elements
Separate
Fine-scale Element
Homogenized Element
?
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Homogenization A Definition of the Error
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Homogenization Error as a Number
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Uniform Mesh Divisions
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Local Homogenization Computations
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Computation Time vs. Element Size
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Computational Time Best Fits
Method A B
CG ICC -4.95 2.73
CG Jacobi -4.82 2.72
Minres ICC -4.96 2.77
Minres Jacobi -4.90 2.82
Sparse Direct -5.09 2.63
Method A B
CG ICC -4.16 4.09
CG Jacobi -4.68 4.50
Minres ICC -4.19 4.14
Minres Jacobi -4.78 4.69
Sparse Direct -5.69 5.91
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Computational Time vs. Element Size
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Total Time for a Newton Step
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Total Time for a Newton Step Remarks
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Total Time for a Newton Step Data 2D
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Total Time for a Newton Step Data 3D
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Remarks
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Compatible Lattice Extensions by Reflections