A weighted reverse Cuthill-McKee procedure for finite element method algorithms to solve strongly anisotropic electrodynamic problems

Journal Article · Tue Feb 01 00:00:00 EST 2011 · Journal of Applied Physics

DOI:https://doi.org/10.1063/1.3516324· OSTI ID:21538073

Cristofolini, Andrea; Latini, Chiara; Borghi, Carlo A ^[1]

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1. Department of Electrical Engineering, University of Bologna, Viale Risorgimento 2, 40136 Bologna (Italy)

This paper presents a technique for improving the convergence rate of a generalized minimum residual (GMRES) algorithm applied for the solution of a algebraic system produced by the discretization of an electrodynamic problem with a tensorial electrical conductivity. The electrodynamic solver considered in this work is a part of a magnetohydrodynamic (MHD) code in the low magnetic Reynolds number approximation. The code has been developed for the analysis of MHD interaction during the re-entry phase of a space vehicle. This application is a promising technique intensively investigated for the shock mitigation and the vehicle control in the higher layers of a planetary atmosphere. The medium in the considered application is a low density plasma, characterized by a tensorial conductivity. This is a result of the behavior of the free electric charges, which tend to drift in a direction perpendicular both to the electric field and to the magnetic field. In the given approximation, the electrodynamics is described by an elliptical partial differential equation, which is solved by means of a finite element approach. The linear system obtained by discretizing the problem is solved by means of a GMRES iterative method with an incomplete LU factorization threshold preconditioning. The convergence of the solver appears to be strongly affected by the tensorial characteristic of the conductivity. In order to deal with this feature, the bandwidth reduction in the coefficient matrix is considered and a novel technique is proposed and discussed. First, the standard reverse Cuthill-McKee (RCM) procedure has been applied to the problem. Then a modification of the RCM procedure (the weighted RCM procedure, WRCM) has been developed. In the last approach, the reordering is performed taking into account the relation between the mesh geometry and the magnetic field direction. In order to investigate the effectiveness of the methods, two cases are considered. The RCM and WRCM procedures has successfully improved the convergence rate of the GMRES solver. For strong anisotropies, the WRCM procedure appears to have a higher convergence rate. The same behavior is shown when applying the methods to the rebuilding of an hypersonic MHD experiment.

• OSTI ID: 21538073
• Journal Information: Journal of Applied Physics, Vol. 109, Issue 3; Other Information: DOI: 10.1063/1.3516324; (c) 2011 American Institute of Physics; ISSN 0021-8979
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
ANISOTROPY
APPROXIMATIONS
CONVERGENCE
ELECTRIC CHARGES
ELECTRIC CONDUCTIVITY
ELECTRIC FIELDS
ELECTRODYNAMICS
FINITE ELEMENT METHOD
INTERACTIONS
ITERATIVE METHODS
LAYERS
MAGNETIC FIELDS
MAGNETIC REYNOLDS NUMBER
MAGNETOHYDRODYNAMICS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA DENSITY
SIMULATION
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
DIMENSIONLESS NUMBERS
ELECTRICAL PROPERTIES
EQUATIONS
FLUID MECHANICS
HYDRODYNAMICS
MATHEMATICAL LOGIC
MATHEMATICAL SOLUTIONS
MECHANICS
NUMERICAL SOLUTION
PHYSICAL PROPERTIES
REYNOLDS NUMBER