Adaptive time-discontinuous Galerkin finite element methods for acoustic scattering

• Published in: The Journal of the Acoustical Society of America Vol. 113; no. 4_Supplement; p. 2252
• Main Authors: He, Dantong, Thompson, Lonny L.
• Format: Journal Article
• Language: English
• Published: 01-04-2003
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.4780414

Comprehensive self-adaptive procedures with efficient sparse multi-level iterative solution algorithms for the time-discontinuous Galerkin space–time finite element method (DGFEM) including high-order accurate nonreflecting boundary conditions (NRBC) are developed for acoustic scattering problems. An h-adaptive space–time strategy is employed based on a superconvergent patch recovery (SPR) technique, together with a temporal error estimate. The use of sub-time steps with pre-integrated local space–time elements to efficiently track waves in space–time are also demonstrated. For accurate data transfer (projection) between meshes, new superconvergent interpolation (SI) procedures are developed. Numerical studies of transient acoustic scattering demonstrate the accuracy, reliability and efficiency gained from the adaptive strategy. [Work supported by NSF.]