Factorized Runge_Kutta_Chebyshev Methods

11th International Conference on Numerical Modeling of Space Plasma Flows

O'Sullivan, Stephen^1

School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland^1

关键词: Acceleration factors;    Composition technique;    Distributed architecture;    Explicit Runge-Kutta methods;    Extended stabilities;    Internal stability;    Large-scale problem;    Stability domains;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/837/1/012020/pdf
DOI  :  10.1088/1742-6596/837/1/012020

来源: IOP

【 摘 要 】

The second-order extended stability Factorized Runge-Kutta-Chebyshev (FRKC2) explicit schemes for the integration of large systems of PDEs with diffusive terms are presented. The schemes are simple to implement through ordered sequences of forward Euler steps with complex stepsizes, and easily parallelised for large scale problems on distributed architectures. Preserving 7 digits for accuracy at 16 digit precision, the schemes are theoretically capable of maintaining internal stability for acceleration factors in excess of 6000 with respect to standard explicit Runge-Kutta methods. The extent of the stability domain is approximately the same as that of RKC schemes, and a third longer than in the case of RKL2 schemes. Extension of FRKC methods to fourth-order, by both complex splitting and Butcher composition techniques, is also discussed. A publicly available implementation of FRKC2 schemes may be obtained from maths.dit.ie/frkc.