论文标题
通过对对角线的1-D无限schrödinger操作员的对角线化，具有分段恒定电势的数值解
Numerical Solution of an Extra-wide Angle Parabolic Equation through Diagonalization of a 1-D Indefinite Schrödinger Operator with a Piecewise Constant Potential
论文作者
论文摘要
我们提出了一种用于计算偏微分方程（PDE）的解的数值方法，用于建模声压，称为宽角抛物线方程，该方程为差异操作员的平方根。差异操作员是具有分段恒定电势的不确定的schrödinger操作员的负。这项工作主要涉及3件案件。但是，将其概括为任意数量的零件。通过限制明智选择的低维子空间，使用近似本征函数来获得操作员特征值的估计值。然后，将估计的特征值用作SECANT方法的初始猜测，以找到确切的特征值，直到圆形误差。然后构建溶液的本征函数扩展。获得每个本征的计算费用与网格大小无关。该方法的准确性，效率和可伸缩性通过数值实验和其他方法进行比较。
We present a numerical method for computing the solution of a partial differential equation (PDE) for modeling acoustic pressure, known as an extra-wide angle parabolic equation, that features the square root of a differential operator. The differential operator is the negative of an indefinite Schrödinger operator with a piecewise constant potential. This work primarily deals with the 3-piece case; however, a generalization is made the case of an arbitrary number of pieces. Through restriction to a judiciously chosen lower-dimensional subspace, approximate eigenfunctions are used to obtain estimates for the eigenvalues of the operator. Then, the estimated eigenvalues are used as initial guesses for the Secant Method to find the exact eigenvalues, up to roundoff error. An eigenfunction expansion of the solution is then constructed. The computational expense of obtaining each eigenpair is independent of the grid size. The accuracy, efficiency, and scalability of this method is shown through numerical experiments and comparisons with other methods.
