## In Preparation or Submitted

- A. Gillman, and P. Geldermans

"An adaptive high order direct solution technique for elliptic boundary value problems," In review. - T. Babb, A. Gillman, S. Hao, and P.G. Martinsson

"An accelerated Poisson solver based on multidomain spectral discretization," In review.

## Publications

- Y. Zhang, and A. Gillman

"A fast direct solver for boundary value problems on locally perturbed geometries,"

To appear in the Journal of Computational and Applied Mathematics.

- 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

- A. Gillman, Fast direct solvers for elliptic partial differential equations, PhD Thesis, CU Boulder, 2011.
- A. Gillman, On the numerical performance of a mixed-hybrid type solution methodology for solving high-frequency Helmholtz problems, Masters Thesis, CSUN, 2006.