Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator
- Courant Institute, New York University, 251 Mercer Street, NY 10012 (United States)
Highlights: {yields} We describe new fast solvers for elliptic partial differential equations in free space. {yields} We combine integral equation methods with Fourier methods to achieve high order accuracy. {yields} We apply these solvers to the evaluation of the Coulomb collision operator in plasma physics. - Abstract: In this paper, we describe a new class of fast solvers for separable elliptic partial differential equations in cylindrical coordinates (r, {theta}, z) with free-space radiation conditions. By combining integral equation methods in the radial variable r with Fourier methods in {theta} and z, we show that high-order accuracy can be achieved in both the governing potential and its derivatives. A weak singularity arises in the Fourier transform with respect to z that is handled with special purpose quadratures. We show how these solvers can be applied to the evaluation of the Coulomb collision operator in kinetic models of ionized gases.
- OSTI ID:
- 21592613
- Journal Information:
- Journal of Computational Physics, Vol. 230, Issue 21; Other Information: DOI: 10.1016/j.jcp.2011.07.005; PII: S0021-9991(11)00409-8; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
COORDINATES
CYLINDRICAL CONFIGURATION
EVALUATION
FOURIER TRANSFORMATION
INTEGRAL EQUATIONS
IONIZED GASES
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
POISSON EQUATION
POTENTIALS
QUADRATURES
SINGULARITY
CONFIGURATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUIDS
GASES
INTEGRAL TRANSFORMATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
TRANSFORMATIONS