In Preparation or Submitted
- N. Beams, A. Gillman, and R. Hewett
"A parallel implementation of a high order accurate solution technique for variable coefficient Helmholtz problems," In review.
- Y. Zhang and A. Gillman
"A fast direct solver for quasi-periodic scattering in multi-layered medium," In preparation.
Publications
- P. Geldermans and A. Gillman
"An adaptive high order direct solution technique for elliptic boundary
value problems," SIAM Journal of Scientific Computing , 41(1), pp. A292-A315, 2019.
- T. Babb, A. Gillman, S. Hao, and P.G. Martinsson
"An accelerated Poisson solver based on multidomain spectral
discretization," BIT Numerical Analysis, 58(4), 851-879, 2018.
- Y. Zhang, and A. Gillman
"A fast direct solver for boundary value problems on locally perturbed
geometries,"
Journal of Computational Physics, 356(1), pp. 356-371, 2018.
- C. Borges, A. Gillman and L. Greengard
"High resolution inverse scattering in two dimensions using recursive
linearization,"
SIAM Journal on Imaging Sciences, 10(2), pp. 641–664, 2017.
- A. Gillman
"An integral equation technique for scattering problems with mixed boundary conditions"
Advances in
Computational Mathematics, 43(2), pp. 351–364, 2017.
- G. Marple, A. Barnett, A. Gillman and S. Veerapaneni
"A Fast Algorithm for Simulating Multiphase Flows Through Periodic Geometries of Arbitrary Shape"
SIAM Journal of Scientific
Computing, 38(5), pp. B740-B772, 2016.
- Y. Chen, Z. Chen, Y. Cheng, A. Gillman and F. Li
"Study of Discrete Scattering Operators for Some Linear Kinetic
Models"
Springer IMA Volume, the
Proceedings for WhAM! A Research Collaboration Workshop for Women in
Numerical Analysis and Scientific Computing, IMA,
Minneapolis, MN, August 11-15, 2014. Accepted, 2015.
- J. Bremer, A. Gillman, and P.G. Martinsson
"A high-order accurate
accelerated direct solver for acoustic scattering from surfaces"
BIT
Numerical Mathematics, 55, pp. 367--397, 2015,
doi:10.1007/s10543-014-0508-y.
- A. Gillman, A. Barnett, and P.G. Martinsson
"A
spectrally
accurate direct solution technique for frequency-domain scattering
problems with variable media"
BIT Numerical Mathematics,
55, pp. 141--170, 2015, doi:10.1007/s10543-014-0499-8.
- A. Gillman and P.G. Martinsson
"A
direct solver with O(N)
complexity for variable coefficient elliptic PDEs
discretized via a high-order composite spectral collocation method''
SIAM Journal of Scientific Computing, 36, pp. A2023-A2046, 2014.
- A. Gillman, and P.G. Martinsson
"An
O(N) algorithm for constructing the solution operator to 2D elliptic
boundary value problems in the absence of body loads"
Advances in Computational
Mathematics 40, pp. 773-796, 2014, doi:10.1007/s10444-013-9326-z.
- A. Gillman and P.G. Martinsson
"A
fast solver for Poisson
problems on infinite regular lattices"
Journal of Computational and Applied Mathematics, 258, pp. 42-56, 2014.
- A. Gillman, S. Hao, and P.G. Martinsson
"A
simplified technique for the efficient and high-order accurate
discretization
of boundary integral equations in 2D on domains with corners"
Journal of Computational Physics, 256, pp. 214–219, 2014.
- A. Gillman, and A. Barnett
"A
fast
direct solver
for quasi-periodic scattering problems"
Journal
of Computational Physics, 248, pp. 309–322, 2013.
- A. Gillman, P. Young, and P.G. Martinsson
"A direct
solver with O(N) complexity for integral equations on one-dimensional
domains"
Frontiers of Mathematics in China, 7, no.
2, pp. 217-247, 2012.
Correction
- A. Gillman, P. Young, P.G. Martinsson
"Numerical
homogenization via approximation of the solution operator"
In B. Engquist, O. Runborg, R. Tsai, editors, Numerical Analysis of
Multiscale Computations, volume 82 of Lecture Notes in
Computational Science and Engineering, Heidelberg, 2011. Springer
Verlag.
- A. Gillman and P.G. Martinsson
"Fast
and accurate numerical methods for solving elliptic difference
equations defined on lattices"
Journal of Computational Physics,
229, no. 24, pp. 9026–9041, 2010.
- A. Gillman, R. Djellouli, and M. Amara
"A Mixed
Hybrid Formulation Based on Oscillated Finite Element Polynomials for
Solving Helmholtz Problems"
Journal of Computational and
Applied Mathematics 204, pp. 515-525, 2007.
Theses