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An algorithm for the direct inversion of the linear systems arising from NystrÃ¶m discretization of integral equations on one-dimensional domains is described. The method typically has O(N) complexityâ€¦ (More)

- Adrianna Gillman, Per-Gunnar Martinsson
- J. Computational Applied Mathematics
- 2014

The Fast Multipole Method (FMM) provides a highly efficient computational tool for solving constant coefficient partial differential equations (e.g. the Poisson equation) on infinite domains. Theâ€¦ (More)

- Adrianna Gillman, Per-Gunnar Martinsson
- Adv. Comput. Math.
- 2014

The large sparse linear systems arising from the finite element or finite difference discretization of elliptic PDEs can be solved directly via, e.g., nested dissection or multifrontal methods. Suchâ€¦ (More)

- Euel Cowan, Richard K. Beatson, +9 authors Martin Titley
- 2003

Traditional method of explicitly defining three-dimensional (3D) ore-waste and geological boundaries relies heavily on a time-consuming process of manual digitisation. This method of modelling can beâ€¦ (More)

- Adrianna Gillman, Alex H. Barnett
- J. Comput. Physics
- 2013

We consider the numerical solution of the scattering of time-harmonic plane waves from an infinite periodic array of reflection or transmission obstacles in a homogeneous background medium, in twoâ€¦ (More)

- Adrianna Gillman, Per-Gunnar Martinsson
- SIAM J. Scientific Computing
- 2014

A numerical method for solving elliptic PDEs with variable coefficients on two-dimensional domains is presented. The method is based on high-order composite spectral approximations and is designedâ€¦ (More)

We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given onâ€¦ (More)

The paper describes techniques for constructing simplified models for problems governed by elliptic equations involving heterogeneous media. Examples of problems under consideration includeâ€¦ (More)

- Carlos Borges, Adrianna Gillman, Leslie Greengard
- SIAM J. Imaging Sciences
- 2017

- Adrianna Gillman, Sijia Hao, Per-Gunnar Martinsson
- J. Comput. Physics
- 2014

where Î“ is a piecewise smooth contour in the plane, and where K is one of the standard kernels of potential theory such as, e.g., the single or double layer kernels associated with the Laplace orâ€¦ (More)