The image-based multiscale multigrid solver, preconditioner, and reduced order model

Abstract

We present a novel image-based multiscale multigrid solver that can efficiently address the computational complexity associated with highly heterogeneous systems. This solver is developed based on an image-based, multiresolution model that enables reliable data flow between corresponding computational grids and provides large data compression. A set of inter-grid operators is constructed based on the microstructural data which remedies the issue of missing coarse grid information. Moreover, we develop an image-based multiscale preconditioner from the multiscale coarse images which does not traverse through any intermediate grid levels and thus leads to a faster solution process. Finally, an image-based reduced order model is designed by prolongating the coarse-scale solution to approximate the fine-scale one with improved accuracy. The numerical robustness and efficiency of this image-based computational framework is demonstrated on a two-dimensional example with high degrees of data heterogeneity and geometrical complexity.