6 papers
What Is the Fractional Laplacian?
Anna Lischke, Guofei Pang, Mamikon Gulian +8
The fractional Laplacian in R^d has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in math…
Hybrid Finite Element - Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver
Mark Ainsworth, Christian Glusa
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed ove…
Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
Mark Ainsworth, Christian Glusa
We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domai…
Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains
Mark Ainsworth, Christian Glusa
We explore the connection between fractional order partial differential equations in two or more spatial dimensions with boundary integral operators to develop techniques that enab…
Is the Multigrid Method Fault Tolerant? The Multilevel Case
Mark Ainsworth, Christian Glusa
Computing at the exascale level is expected to be affected by a significantly higher rate of faults, due to increased component counts as well as power considerations. Therefore, c…
Is the Multigrid Method Fault Tolerant? The Two-Grid Case
Mark Ainsworth, Christian Glusa
The predicted reduced resiliency of next-generation high performance computers means that it will become necessary to take into account the effects of randomly occurring faults on…