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首页> 外文期刊>Journal of Computational Physics >The effective conductivity of arrays of squares: Large random unit cells and extreme contrast ratios
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The effective conductivity of arrays of squares: Large random unit cells and extreme contrast ratios

机译：正方形阵列的有效电导率：大型随机晶胞和极高的对比度

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摘要

An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends recent work on multi-component checkerboards at medium contrast ratios. General improvement include the simplification of a long-range preconditioner, the use of a banded solver, and a more efficient placement of quadrature points. This, together with a reduction in the number of unknowns, allows for a substantial increase in achievable accuracy as well as in tractable system size. Results, accurate to at least nine digits, are obtained for random checkerboards with over a million squares in the unit cell at contrast ratio 10~6. Furthermore, the scheme is flexible enough to handle complex valued conductivities and, using a homotopy method, purely negative contrast ratios. Examples of the accurate computation of resonant spectra are given.
机译：提出了一种基于积分方程的方案，用于以非常高的对比度快速，准确地计算具有复杂晶胞的两组分棋盘状复合材料的有效电导率。该方案以中等对比度扩展了最近在多组分棋盘上的工作。总体改进包括简化远程预处理器，使用带状求解器以及更有效地放置正交点。这与未知数数量的减少一起，可以大大提高可达到的精度以及易于处理的系统大小。对于对比度为10〜6的晶胞中超过一百万个正方形的随机棋盘，可获取至少9位数字的结果。此外，该方案足够灵活，可以处理复杂的电导率值，并使用同伦方法来纯负对比度。给出了精确计算共振光谱的示例。

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