Fast time‐explicit micro‐heterogeneous wave propagation. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Maier, Roland; Peterseim, Daniel
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800294
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Using explicit time stepping schemes in the context of wave propagation is very popular due to simplicity and fast computations. However, stability can only be guaranteed if a so‐called CFL condition holds that bounds the time step size with respect to the spatial mesh size. This is a severe restriction in case of micro‐heterogeneous media where spatial finescale features need to be resolved. We show how numerical homogenization in space both reduces the number of degrees of freedom in space and weakens the time step restriction.