Adrianna Gillman

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Contact Information

Office: Kemeny Hall 210
Address: Department of Mathematics, 27 Main St., Hanover, NH
Email: adrianna.gillman (at) dartmouth.edu
Office hours: M 2:30-4 pm, F 1:30-3pm or by appointment

Teaching

Winter 2012: Math 23 Differential Equations
Fall 2011: Math 8 Calculus of Functions of One and Several Variables

Research Interests

Numerical Analysis
Numerical methods for solving elliptic partial differential equations
Fast algorithms such as fast multipole methods and techniques for Hierarchal Semi-separable matrices
Mathematical modeling of physics and other real world applications

Education

    Ph.D. in Applied Mathematics, University of Colorado at Boulder (CU Boulder), August 2011
    Advisor: Per-Gunnar Martinsson
    M.S. in Applied Mathematics, California State University, Northridge (CSUN), June 2006
    Advisor: Rabia Djellouli
    B.S. in Applied Mathematics, CSUN, May 2003

Publications

In Refereed Journal

  1. A. Gillman, and P.G. Martinsson, "An O(N) algorithm for constructing the solution operator to elliptic boundary value problems in the absence of body loads". Submitted.
  2. A. Gillman, and P.G. Martinsson, "A fast solver for Poisson problems on infinite regular lattices". Submitted.
  3. A. Gillman, P. Young, and P.G. Martinsson, "A direct solver with O(N) complexity for integral equations on one-dimensional domains". To appear in Frontiers of Mathematics in China.
  4. A. Gillman and P.G. Martinsson, "Fast and accurate numerical methods for solving elliptic difference equations defined on lattices", Journal of Computational Physics 229 (2010), no. 24, 9026–9041.
  5. 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 (2007), pp. 515-525.

In Conference Proceedings

  1. 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.

Thesis

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