Fast numerical treatment of nonlinear wave equations by spectral methods

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.3551464· OSTI ID:21535141

Skjaeraasen, Olaf ^[1]; Robinson, P A ^[2]; Newman, D L ^[3]

---

1. ProsTek, Institute for Energy Technology, P.O. Box 40, N-2027 Kjeller (Norway)
2. School of Physics, University of Sydney, New South Wales 2006 (Australia)
3. Center for Integrated Plasma Studies, University of Colorado at Boulder, Boulder, Colorado 80309 (United States)

A method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high- and low-frequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is mode-dependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schroedinger equation applies.

• OSTI ID: 21535141
• Journal Information: Physics of Plasmas, Vol. 18, Issue 2; Other Information: DOI: 10.1063/1.3551464; (c) 2011 American Institute of Physics; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
DAMPING
EIGENFUNCTIONS
EIGENVALUES
EIGENVECTORS
FINITE DIFFERENCE METHOD
NONLINEAR PROBLEMS
PLASMA WAVES
SCHROEDINGER EQUATION
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
ITERATIVE METHODS
MATHEMATICAL SOLUTIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS