Parallel Numerical Methods for Solving Nonlinear Evolution Equations
نویسندگان
چکیده
Nonlinear evolution equations are of tremendous interest in both theory and applications. In this talk we introduce parallel algorithms for numerical simulations of CMKdV, NLS and and CNLS equations in 1+1 and 1+2 dimensions. The parallel methods are implemented on multiprocessor system. Numerical experiments have shown that these methods give accurate results and considerable speedup. This talk is organized as follows: • Introduction to the NLS and CNLS equations • The split-step method and Fourier transform. • Numerical methods for the NLS and CNLS equations. • Numerical methods for the CMKdV equation. • Numerical methods for (1+2) NLS. • Parallel Numerical methods for the KdV-Like equations. Nonlinear Schrödinger Equations The nonlinear Schrödinger(NLS) and the coupled nonlinear Schrödinger (CNLS) equations are of tremendous interest in both theory and applications. Various regimes of pulse propagation in optical fibers are modeled by some form of the NLS type equation. The CNLS equation is the governing equation for the propagation of two orthogonally polarized pulses in a monomode birefringent fibers. In this presentation, different numerical methods will be presented for numerical simulations of the above equations. More emphasis will be on the design and implementation of parallel split-step Fourier methods for these equations. These parallel methods are implemented on the Origin 2000 multiprocessor computer. Our numerical experiments have shown that these methods give accurate results and considerable speedup.
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