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Abstract <p>We have proposed and investigated a parallelization of the computational scheme for integrating the time-dependent three-dimensional Schrödinger equation in the discrete variable representation (DVR). When expanded in a two-dimensional DVR basis, the original three-dimensional equation is reduced to a system of ordinary differential equations of the Schrödinger type. The method of component-by-component splitting is applied for its numerical integration, ensuring computational efficiency by separating the problem into independent subproblems. The study demonstrates that the most computationally expensive steps of the procedure, namely, transforming the vector of the sought solutions from the DVR to the spherical function representation and vice versa at each time-step, can be efficiently parallelized. Results of the numerical simulation are presented, showing a significant reduction in computation time for problems requiring a large number of grid points when approximating the original problem in both temporal and spatial variables.</p>

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Parallelization of Computational Scheme Based on Two-Dimensional DVR for Integrating Time-Dependent Three-Dimensional Schrödinger Equation

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. S. Ayriyan,
  • J. Buša Jr.,
  • V. S. Melezhik

摘要

Abstract

We have proposed and investigated a parallelization of the computational scheme for integrating the time-dependent three-dimensional Schrödinger equation in the discrete variable representation (DVR). When expanded in a two-dimensional DVR basis, the original three-dimensional equation is reduced to a system of ordinary differential equations of the Schrödinger type. The method of component-by-component splitting is applied for its numerical integration, ensuring computational efficiency by separating the problem into independent subproblems. The study demonstrates that the most computationally expensive steps of the procedure, namely, transforming the vector of the sought solutions from the DVR to the spherical function representation and vice versa at each time-step, can be efficiently parallelized. Results of the numerical simulation are presented, showing a significant reduction in computation time for problems requiring a large number of grid points when approximating the original problem in both temporal and spatial variables.