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Alexander H. Barnett

Assistant Professor of Mathematics
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Departments and Programs

  • Mathematics

Related Links

Contact Information

Email: alexander.barnett@dartmouth.edu
Phone: 603-646-3178
Office: 6188 Kemeny Hall

Education

B.A. Cambridge University; Ph.D. Harvard University

Areas of Expertise

Efficient computational methods for partial differential equations; eigenvalues of the Laplacian, high frequency waves, photonic crystals, boundary integral methods, parabolic equations in complex geometries; spectral properties of quantized chaotic dynamical systems, billiards; mathematical ecology, animal home range modeling; inverse problems in medical imaging: Diffuse Optical Tomography, Bayesian statistical inversion.

Selected Works

  • Barnett, A H and T Betcke, "Stability and Convergence of the Method of Fundamental Solutions for Helmholtz Problems on Analytic Domains," Journal of Computational Physics, 227:14 (2008) 7003-7026.
  • Barnett, A H and P R Moorcroft, "Analytic Steady-State Space Use Patterns and Rapid Computations in Mechanistic Home Range Analysis," Journal of Mathematical Biology, 57:1 (2008) 139-159.
  • Barnett, A H and T Betcke, "Quantum Mushroom Billiards," CHAOS, 17:4 (2007) 043123.
  • "Asymptotic Rate of Quantum Ergodicity in Chaotic Euclidean Billiards," Communications on Pure and Applied Mathematics, 59:10 (October 2006) 1457-1488.
  • "A Fast Numerical Method for Time-Resolved Photon Diffusion in General Stratified Turbid Media," Journal of Computational Physics, 201 (2004) 771-797.

Current Projects

"Perturbative Analysis of the Method of Particular Solutions for Improved Inclusion of High-Lying Dirichlet Eigenvalues;" "Photonic Band Structure Calculations Using Second-Kind Integral Equations (joint with L Greengard, NYU)"