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首页> 外文期刊>Journal of Computational Physics >Numerical methods for computing ground states and dynamics of nonlinear relativistic Hartree equation for boson stars
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Numerical methods for computing ground states and dynamics of nonlinear relativistic Hartree equation for boson stars

机译：玻色子恒星非线性相对论哈特里方程的基态和动力学计算的数值方法

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摘要

Efficient and accurate numerical methods are presented for computing ground states and dynamics of the three-dimensional (3D) nonlinear relativistic Hartree equation both without and with an external potential. This equation was derived recently for describing the mean field dynamics of boson stars. In its numerics, due to the appearance of pseudodifferential operator which is defined in phase space via symbol, spectral method is more suitable for the discretization in space than other numerical methods such as finite difference method, etc. For computing ground states, a backward Euler sine pseudospectral (BESP) method is proposed based on a gradient flow with discrete normalization; and respectively, for computing dynamics, a time-splitting sine pseudospectral (TSSP) method is presented based on a splitting technique to decouple the nonlinearity. Both BESP and TSSP are efficient in computation via discrete sine transform, and are of spectral accuracy in spatial discretization. TSSP is of second-order accuracy in temporal discretization and conserves the normalization in discretized level. In addition, when the external potential and initial data for dynamics are spherically symmetric, the original 3D problem collapses to a quasi-1D problem, for which both BESP and TSSP methods are extended successfully with a proper change of variables. Finally, extensive numerical results are reported to demonstrate the spectral accuracy of the methods and to show very interesting and complicated phenomena in the mean field dynamics of boson stars.
机译：提出了有效而精确的数值方法，用于计算有外部势能和无外部势力的三维（3D）非线性相对论哈特里方程的基态和动力学。最近推导了这个方程，用于描述玻色子恒星的平均场动力学。在其数值上，由于出现了通过符号在相空间中定义的伪微分算子，因此频谱方法比其他数值方法（例如有限差分法等）更适合于空间离散化。对于计算基态，后向欧拉提出了一种基于离散归一化梯度流的正弦伪谱（BESP）方法。分别为计算动力学，提出了一种基于分裂技术的时间分裂正弦伪谱（TSSP）方法，以解耦非线性。 BESP和TSSP都可以通过离散正弦变换高效地进行计算，并且在空间离散化方面具有频谱准确性。 TSSP在时间离散化方面具有二阶精度，并且在离散化水平上保留了规范化。另外，当外部势能和动力学的初始数据是球对称的时，原始的3D问题崩溃为准1D问题，对于BESP和TSSP方法，可以通过适当地更改变量来成功扩展它们。最后，据报道，大量的数值结果证明了该方法的光谱准确性，并在玻色子恒星的平均场动力学中显示出非常有趣和复杂的现象。

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