Efficient Reconstruction of Multi-Phase Morphologies from Correlation Functions
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Efficient Reconstruction of Multi-Phase Morphologies from Correlation Functions Michael G. Rozmanā and Marcel Utz Institute of Materials Science and Department of Physics, University of Connecticut ABSTRACT A highly efficient algorithm for the reconstruction of microstructures of heterogeneous media from spatial correlation functions is presented. Similar to previously proposed algorithms, the new method relies on Monte Carlo optimization, representing the microstructure on a discrete grid. An efficient way to update the correlation functions after local changes to the structure is introduced. In addition, the rate of convergence is substantially enhanced by selective Monte Carlo moves at interfaces. Speedups over prior methods of more than two orders of magnitude are thus achieved. The algorithm is ideally suited for parallel computers. The increase in efficiency brings new classes of problems within the realm of the tractable, notably those involving several different structural length scales and/or components. INTRODUCTION Heterogeneous media, such as composites, porous materials, or polymer blends, often exhibit complex microstructures, which are intimately related to their properties. Many important characterization techniques provide morphological information in the form of spatial correlation functions. However, a real-space microstructural model is needed for understanding and predicting material properties. Therefore, finding microstructures consistent with a given correlation function is important for both materials science and technology. Several different approaches have been taken to solve this inverse problem (see recent reviews [1, 2]). Recently Torquato and co-workers [3, 4] have proposed a stochastic reconstruction procedure, based on discretization of the spatial structure on a grid, each pixel of which is attributed to a single phase. The method departs from an arbitrary configuration, and then minimizes the discrepancy between the actual and target correlation functions by simulated annealing. The correlation function is continuously updated using the Fast Fourier Transform (FFT). While this discrete stochastic minimization approach is attractive due to its generality and flexibility, its main disadvantage lies in the high computational cost. The computational complexity severely limits the applicability of the method to systems which require high resolutions or which are composed of more than two phases. In the present contribution, we describe a discrete minimization algorithm for restoration that avoids these shortcomings. The algorithm uses a method to update the correlation function much faster than the FFT. This is possible by re-using the correlation function from the previous configuration, rather than recomputing it from scratch. In addition, candidate pixels for the Monte Carlo moves are chosen exclusively at phase boundaries, and a minimization method different from the traditional simulated annealing protocol is used. These improvements together lead to speedups of more than two order
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