Symbolic vector analysis in plasma physics

• Published in: Computer physics communications Vol. 116; no. 1; pp. 107 - 120
• Main Authors: Qin, H., Tang, W.M., Rewoldt, G.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-01-1999; Elsevier Science
• Subjects: Computational techniques; Computer algebra; Exact sciences and technology; Mathematica; Mathematical methods in physics; Other topics in mathematical methods in physics; Physics; Physics of gases, plasmas and electric discharges; Physics of plasmas and electric discharges; Plasma physics; Vector analysis; Mathematica; Plasma physics; Vector analysis; Computer algebra; Fluid dynamics; Mathematical analysis; Vector calculus; Theoretical study; Coordinate system; Symbolic computation
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/S0010-4655(98)00144-1

Many problems in plasma physics involve substantial amounts of analytical vector calculation. The complexity usually originates from both the vector operations themselves and the underlying coordinate systems. A computer algebra package for symbolic vector analysis in general coordinate systems, GeneralVectorAnalysis (GVA), is developed using Mathematica. The modern viewpoint for 3D vector calculus, differential forms on 3-manifolds, is adopted to unify and systematize the vector calculus operations in general coordinate systems. Besides the basic vector analysis functions, the package provides asymptotic capabilities, 2D vector analysis notation, and a simple interface for users to define their own coordinate systems. These features will benefit physicists and applied mathematicians in their research where complicated vector analysis in complicated coordinate systems is required. Several applications of this symbolic vector analysis package to plasma physics are also given.