{"paper":{"title":"Multi-level Monte Carlo acceleration of computations on multi-layer materials with random defects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Erik von Schwerin, Petr Plech\\'a\\v{c}","submitted_at":"2016-11-29T18:51:43Z","abstract_excerpt":"We propose a Multi-level Monte Carlo technique to accelerate Monte Carlo sampling for approximation of properties of materials with random defects.\n  The computational efficiency is investigated on test problems given by tight-binding models of a single layer of graphene or of $MoS_2$ where the integrated electron density of states per unit area is taken as a representative quantity of interest.\n  For the chosen test problems the multi-level Monte Carlo estimators significantly reduce the computational time of standard Monte Carlo estimators to obtain a given accuracy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09784","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}