A Modulus-Squared Dirichlet Boundary Condition for Time-Dependent Complex Partial Differential Equations and its Application to the Nonlinear Schödinger Equation

A Modulus-Squared Dirichlet Boundary Condition for Time-Dependent Complex Partial Differential Equations and its Application to the Nonlinear Schödinger Equation
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DOI：
10.1137/130920046
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发表时间：
2011-10
期刊：
SIAM J. Sci. Comput.
影响因子：
--
通讯作者：
R. Caplan;R. Carretero-González
R. Caplan;R. Carretero-González
中科院分区：
其他
文献类型：
--
作者：
R. Caplan;R. Carretero-González

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提出了一种易于实现的模平方Dirichlet（MSD）边界条件，用于数值模拟多维环境中的含时复偏微分方程。MSD边界条件近似于边界处解的常数模平方值。将MSD边界条件应用于非线性Schr odinger方程，并通过数值模拟验证了MSD边界条件的有效性和优越性.
An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a constant modulus-square value of the solution at the boundaries. Application of the MSD boundary condition to the nonlinear Schr\"odinger equation is shown, and numerical simulations are performed to demonstrate its usefulness and advantages over other simple boundary conditions.