Fetching the paper…

Reading the bibliography…

Fast Poisson solvers for spectral methods · Around

2017

Fast Poisson solvers for spectral methods

Fortunato, Daniel, Townsend, Alex

Original
PDF
Post on X

Understand

Poisson's equation is the canonical elliptic partial differential equation.

While there exist fast Poisson solvers for finite difference and finite element methods, fast Poisson solvers for spectral methods have remained elusive.
Here, we derive spectral methods for solving Poisson's equation on a square, cylinder, solid sphere, and cube that have an optimal complexity (up to polylogarithmic terms) in terms of the degrees of freedom required to represent the solution.
Whereas FFT-based fast Poisson solvers exploit structured eigenvectors of finite difference matrices, our solver exploits a separated spectra property that holds for our spectral discretizations.

Built on

S. Gershgorin
1931
Earlier work this paper cites.
D. W. Peaceman and J. H. H. Rachford
1955
Earlier work this paper cites.
B. L. Buzbee, G. H. Golub, and C. W. Nielson
1970
Earlier work this paper cites.
R. H. Bartels and G. W. Stewart
1972
Earlier work this paper cites.
P. E. Merilees
1973
Earlier work this paper cites.
V. I. Lebedev
1977
Earlier work this paper cites.
D. B. Haidvogel and T. Zang
1979
Earlier work this paper cites.
P. Henrici
1979
Earlier work this paper cites.
J. A. C. Weideman and L. N. Trefethen
1988
Earlier work this paper cites.
A. Lu and E. L. Wachspress
1991
Earlier work this paper cites.
E. Wachspress
1994
Earlier work this paper cites.
A. McKenney, L. Greengard, and A. Mayo
1995
Earlier work this paper cites.
L. Greengard and J. Lee
1996
Earlier work this paper cites.

Similar

A. Averbuch, M. Israeli, and L. Vozovoi
1998
Cited alongside, same era.
E. Braverman, M. Israeli, A. Averbuch, and L. Vozovoi
1998
Cited alongside, same era.
D. J. Torres and E. A. Coutsias
1999
Cited alongside, same era.
L. N. Trefethen
2000
Cited alongside, same era.
J. P. Boyd
2001
Cited alongside, same era.
P. G. Martinsson, V. Rokhlin, and M. Tygert
2005
Cited alongside, same era.
R. J. LeVeque
2007
Cited alongside, same era.
J. Sabino

Then

A. Townsend and L. N. Trefethen
2013
Later among the works it cites.
E. Wachspress
2013
Later among the works it cites.
T. A. Driscoll, N. Hale, and L. N. Trefethen
2014
Later among the works it cites.
S. Olver and A. Townsend
2014
Later among the works it cites.
A. Townsend and S. Olver
2015
Later among the works it cites.
A. Gholami, D. Malhotra, H. Sundar, and G. Biros
2016
Later among the works it cites.
A. Townsend, H. Wilber, and G. B. Wright
2016
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

2007

Cited alongside, same era.

P. Benner, R.-C. Li, and N. Truhar

2009

Cited alongside, same era.

V. Britanak, P. C. Yip, and K. R. Rao

2010

Cited alongside, same era.

B. N. Datta

2010

Cited alongside, same era.

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark

2010

Cited alongside, same era.

H. Wilber

2016

Later among the works it cites.

B. Beckermann and A. Townsend

2017

Closest in time.

GitHub repository, 2017, https://github.com/danfortunato/fast-poisson-solvers

D. Fortunato and A. Townsend · 2017

Closest in time.

A. Townsend, M. Webb, and S. Olver

2017

Closest in time.

H. Wilber, A. Townsend, and G. B. Wright

2017

Closest in time.