Parallel solver for the time-dependent linear and nonlinear Schrödinger equation.
Parallel solver for the time-dependent linear and nonlinear Schrödinger equation.
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DOI：
10.1103/physreve.73.036708
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发表时间：
2006-03
期刊：
影响因子：
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通讯作者：
B. Schneider;L. Collins;Suxing Hu
中科院分区：
文献类型：
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作者：
B. Schneider;L. Collins;Suxing Hu
物理和化学中的各种问题都需要求解与时间相关的薛定谔方程。这些包括随时间变化的电磁场中的原子和分子、原子碰撞问题的随时间变化的方法，以及描述材料受到内力和外力的行为。我们描述了一种将有限元离散变量表示（FEDVR）与实空间乘积（RSP）算法相结合的方法，以生成一种高效且高精度的方法来求解瞬态线性和非线性薛定谔方程。 FEDVR 使用最少数量的网格点提供高度准确的空间表示，而 RSP 算法则在每个时间步的操作中传播波函数。该方法的并行化是透明的，并且通过在消息传递接口方案内跨可用处理器分布一或两个空间维度来实现。给出了完整的形式主义和大量的三维例子；通过与常用的有限差分法的比较，说明了其高精度和有效性。
A solution of the time-dependent Schrödinger equation is required in a variety of problems in physics and chemistry. These include atoms and molecules in time-dependent electromagnetic fields, time-dependent approaches to atomic collision problems, and describing the behavior of materials subjected to internal and external forces. We describe an approach in which the finite-element discrete variable representation (FEDVR) is combined with the real-space product (RSP) algorithm to generate an efficient and highly accurate method for the solution of the time-dependent linear and nonlinear Schrödinger equation. The FEDVR provides a highly accurate spatial representation using a minimum number of grid points while the RSP algorithm propagates the wave function in operations per time step. Parallelization of the method is transparent and is implemented here by distributing one or two spatial dimensions across the available processors, within the message-passing-interface scheme. The complete formalism and a number of three-dimensional examples are given; its high accuracy and efficacy are illustrated by a comparison with the usual finite-difference method.