Dr. Graham Kaland
FB Mathematik und Informatik
Numerical Analysis of Partial Differential Equations
November 2016 - present: Postdoctoral research with Prof. Ralf Kornhuber's group here at Freie Universität Berlin
2013 - October 2016: Postdoctoral research with Prof. Martin Frank's group at MathCCES, RWTH Aachen University
Wintersemester 2015/2016: Temporary professor at MathCCES, RWTH Aachen University
2002 - 2007: BS / MS in Systems and Control Engineering at Case Western Reserve University, Cleveland, Ohio (Advisor: Michael S. Branicky)
Moment closures for kinetic equations:
- Robust numerical methods for the moment-constrained entropy minimization problem
- Moment realizability conditions (generalizations of the Hausdorff moment problem)
- Realizability limiting
- Novel moment-defining bases
- Numerical methods for the resulting PDEs
Pichard, T. and Alldredge, G. W. and Brull, S. and Dubroca, B. and Frank, M. (2016) An approximation of the M_2 closure: application to radiotherapy dose simulation. To Appear in Journal of Scientific Computing.
Kyrion, T. and Alldredge G. W. (2016) Robust inversion methods for aerosol spectroscopy. [arXiv:1606.01293]. Inverse Problems in Science and Engineering, 1-39.
Alldredge, G. W. and Li, R. and Li, W. (2016) Approximating the M_2 method by the extended quadrature method of moments for radiative transfer in slab geometry. Kinetic and Related Models, 9 (2). pp. 237-249. [arXiv:1507.01676]
Schneider, F. and Alldredge, G. and Kall, J. (2016) A realizability-preserving high-order kinetic scheme using WENO reconstruction for entropy-based moment closures of linear kinetic equations in slab geometry. Kinetic and Related Models, 9 (1). pp. 193-215. ISSN Print: 1937-5093 [arXiv:1501.07765]
Alldredge, G. and Schneider, F. (2015) A realizability-preserving discontinuous Galerkin scheme for entropy-based moment closures for linear kinetic equations in one space dimension. Journal of Computational Physics, 295. pp. 665-684. [arXiv:1501.03660]; Supplementary material: Counting the number of facets in the numerically realizable set
Schneider, F. and Alldredge, G. W. and Frank, M. and Klar, A. (2014) Higher order mixed moment approximations for the Fokker-Planck equation in one space dimension. SIAM Journal on Applied Mathematics, 74 (4). pp. 1087-1114. [arXiv:1405.5305]
Alldredge, G. W. and O'Leary, D. P. and Hauck, C. D. and Tits, A. L. (2014) Adaptive change of basis in entropy-based moment closures for linear kinetic equations. Journal of Computational Physics, 258. pp. 489-508. [arXiv:1306.2881]
Alldredge, G. W. and Hauck, C. D. and Tits, A. L. (2012) High-order entropy-based closures for linear transport in slab geometry II: A computational study of the optimization problem. SIAM Journal on Scientific Computing, 34 (4). pp. B361-B391.