N-dimensional error control multiresolution algorithms for the point value discretization

J. García, J.A. Padilla, J. Ruiz and J.C. Trillo

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 170, issue C, 79-97

Abstract: In this paper we present N-dimensional multiresolution algorithms with and without error control strategies in the point values setting. This work complements the case of cell averages (Ruiz and Trillo, 2017). It can be somehow considered a generalization to N dimensions of several works, see Harten (1993), Harten (1996), Claypoole et al. (2003) [12], Amat et al. (2002). Apart from presenting the N-dimensional algorithms, we focus mainly on three concerns. Firstly, on deriving the corresponding results proving the stability and giving explicit error bounds. Secondly on explaining in some detail how to carry out the programming, and finally we include some interesting numerical experiments in various dimensions. In particular, we present a different application for each dimension up to N=5. They have been chosen to let clear the wide range of possible applications of these algorithms. In 1D we present an experiment where it is crucial to gain in computational time. In 2D, we deal with the compression and reconstruction of contour maps representing the topography of a certain terrain such as a seabed. In 3D, a scalar physical property, namely the salinity, is measured in a three dimensional mesh and then kept to be reconstructed later in time and compared with new measurements. In 4D, we deal with a temperature field in a cylindrical pipe in a heat exchanger. This field occupies a lot of memory inside a finite elements calculation, and a possibility to deal with this fact is to compress this field or to use the information given by the multiresolution coefficients to save computational time by refining the mesh just in the necessary zones. In 5D we work with a splitted sinusoidal function, which exemplifies a similar situation to the 2D contour map, but in a higher dimension.

Keywords: Multiresolution; Several dimensions; Point values; Error control; Nonlinearity (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475419302198
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:170:y:2020:i:c:p:79-97

DOI: 10.1016/j.matcom.2019.07.004

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().