Developed high performance distributed algorithms for the solution
of hyperbolic conservation laws, with focus on plasma science
applications. The algorithms are being used to study moment-equations of the Vlasov-Maxwell equations. The
application is written in C++ and is scripted in Python and runs on
parallel clusters using the Message Passing Interface (MPI)
library. This work was funded by the Air-Force Office of
Scientific Research and has resulted in two publications in the
Journal of Computational Physics and several conference proceedings.
Wrote a compiler for a strongly typed language of the ML family. The
language has complete formal semantics, supports automatic type
inference, continuations, garbage collection and a module
system. The language was designed to study problems in Algorithmic
Information theory.
Developed an accurate semi-analytical discrete ordinates algorithm
to compute light fields in participating media. The code has
applications to realistic physics-based computer graphics and
biomedical optics. Used the code to study underwater light
distributions inside the ocean bounded by a stochastic wave-driven
surface. Algorithms are implemented as a C++ class library scripted
using the Python programming language.
Developed inverse algorithms and software implementing the
algorithms to determine optical properties of light scattering
media. This work has application to ocean water optics and realistic
light scattering from surfaces, and has resulted in two publications
in Applied Optics. The application was written in C++.
Expert in computational physics, finite volume methods and
Discontinuous Galerkin finite element methods as applied to
numerical solutions of hyperbolic conservation laws.
Expert in computational plasma physics.
Advanced knowledge of modern programming language theory, formal
specification using operational and denotational semantics and
automatic type inference.
Parallel programming with the Message Passing Interface.
Expert in C/C++, Python programming languages. Advanced
C++ programming techniques: template meta-programming, generic
programming.
Expert in OCaml, Scheme and Common Lisp programming languages.
Knowledge of advanced web-programming techniques using continuations
and functional techniques.
A. Hakim, J. Loverich, U. Shumlak, "A High Resolution Wave
Propagation Scheme for ideal Two-Fluid Plasma Equations", Journal of
Computational Physics. Available online.
J. Loverich, A. Hakim, U. Shumlak, "A Discontinuous Galerkin
method for ideal Two-Fluid Plasma Equations", Journal of
Computational Physics. To appear
A.H. Hakim B.D. Piening and N.J. McCormick. "Near-asymptotic angle
dependence of ocean optical radiance", Applied Optics, 43,
(2004)
A.H. Hakim and N.J. McCormick. "Ocean optics estimation for
absorption, backscattering, and phase function parameters", Applied
Optics, 42, 931-938 (2003)
A. Hakim, U. Shumlak, "A High Resolution Wave Propagation Scheme for
Two-Fluid Plasma equations with Applications to Field Reversed
Configurations.", APS Division of Plasma Physics Conference, Denver,
Colorado, (October 2005).
A. Hakim, U. Shumlak, "A High Resolution Scheme for Two-Fluid Plasma
model", IEEE Conference on Plasma Physics, Monterey, California,
(June 2005).
A. Hakim, U. Shumlak, "A High Resolution Scheme for the
Two-Fluid Plasma Equations", American Physical Society Conference on
Plasma Physics, Savannah, Georgia, (Nov 2004)
A. Hakim, U. Shumlak, "Maxwell Equation Solver for Plasma
Simulations Based on Mixed Potential Formulation", 16th AIAA-CFD
Conference, Orlando Florida. (2003). AIAA paper number 2003-3829