{"paper":{"title":"A k-space method for nonlinear wave propagation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Greg. T. Clement, Yun Jing","submitted_at":"2011-05-11T14:43:09Z","abstract_excerpt":"A k-space method for nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme [Mast et al., IEEE Tran. Ultrason. Ferroelectr. Freq. Control 48, 341-354 (2001)]. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to the finite element method. It is found that, in order to obtain accurate results in homogeneous media, the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2210","kind":"arxiv","version":2},"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"}