Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains

Mark Ainsworth () and Christian Glusa ()
Additional contact information
Mark Ainsworth: Brown University, Division of Applied Mathematics
Christian Glusa: Sandia National Laboratories, Center for Computing Research

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 17-57 from Springer

Abstract: Abstract We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enable one to efficiently tackle the integral fractional Laplacian. In particular, we develop techniques for the treatment of the dense stiffness matrix including the computation of the entries, the efficient assembly and storage of a sparse approximation and the efficient solution of the resulting equations. The main idea consists of generalising proven techniques for the treatment of boundary integral equations to general fractional orders. Importantly, the approximation does not make any strong assumptions on the shape of the underlying domain and does not rely on any special structure of the matrix that could be exploited by fast transforms. We demonstrate the flexibility and performance of this approach in a couple of two-dimensional numerical examples.

Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:spr:sprchp:978-3-319-72456-0_2

Ordering information: This item can be ordered from
http://www.springer.com/9783319724560

DOI: 10.1007/978-3-319-72456-0_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().