Fast Numerical Coarsening with Local Factorizations

Abstract

Numerical coarsening methods offer an attractive methodology for fast simulation of objects with high-resolution heterogeneity. However, they rely heavily on preprocessing, and are not suitable when objects undergo dynamic material or topology updates. We present methods that largely accelerate the two main processes of numerical coarsening, namely training data generation and the optimization of coarsening shape functions, and as a result we manage to leverage runtime numerical coarsening under local material updates. To accelerate the generation of training data, we propose a domain-decomposition solver based on substructuring that leverages local factorizations. To accelerate the computation of coarsening shape functions, we propose a decoupled optimization of smoothness and data fitting. We evaluate quantitatively the accuracy and performance of our proposed methods, and we show that they achieve accuracy comparable to the baseline, albeit with speed-ups of orders of magnitude. We also demonstrate our methods on example simulations with local material and topology updates.