Multiscale direction-splitting algorithms for parabolic equations with highly heterogeneous coefficients

abstract

• 2016 Elsevier Ltd In this paper we discuss two methods for upscaling of highly heterogeneous data for parabolic problems in the context of a direction splitting time approximation. The first method is a direct application of the idea of Jenny et al. (2003) in the context of the direction splitting approach. The second method devises the approximation from the Schur complement corresponding to the interface unknowns of the coarse grid, by applying a proper L 2 projection operator to it. The spatial discretization employed in this paper is based on a MAC finite volume stencil but the same approach can be implemented within a proper finite element discretization. A key feature of the present approach is that it can extend to 3D problems with very little computational overhead. The properties of the resulting approximations are demonstrated numerically on some benchmark coefficient data available in the literature.

authors

• Lazarov, Raytcho

published proceedings

• COMPUTERS & MATHEMATICS WITH APPLICATIONS

author list (cited authors)

• Srinivasan, S., Lazarov, R., & Minev, P.

citation count

• 4

complete list of authors

• Srinivasan, Shriram||Lazarov, Raytcho||Minev, Peter

publication date

• January 2016

publisher

• Elsevier  Publisher

published in

• Computers and Mathematics with Applications  Journal

keywords

• Direction-splitting
• Multiscale Methods
• Parabolic Equations

Digital Object Identifier (DOI)

• 10.1016/j.camwa.2016.07.032

start page

• 1641

end page

• 1654

volume

• 72

issue

• 6

URL

• http://dx.doi.org/10.1016/j.camwa.2016.07.032