{"paper":{"title":"Theory and implementation of $\\mathcal{H}$-matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"math.NA","authors_text":"Luca Desiderio (POEMS), Patrick Ciarlet (POEMS), St\\'ephanie Chaillat (POEMS)","submitted_at":"2017-06-22T06:31:38Z","abstract_excerpt":"In this work, we study  the accuracy and efficiency of hierarchical matrix ($\\mathcal{H}$-matrix) based fast methods for solving dense linear systems arising from the discretization of the 3D elastodynamic Green's tensors. It is well known in the literature that standard  $\\mathcal{H}$-matrix based methods,  although very efficient tools for asymptotically smooth kernels, are  not optimal for oscillatory kernels. $\\mathcal{H}^2$-matrix and  directional approaches have been proposed to overcome this problem. However the implementation of such methods is much more involved than the standard $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09384","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"}