In this work we present a space-time least squares isogeometric discretization of the Schr\"odinger equation and propose a preconditioner for the arising linear system in the parametric domain. Exploiting the tensor product structure of the basis functions, the preconditioner is written as the sum of Kronecker products of matrices. Thanks to an extension to the classical Fast Diagonalization method, the application of the preconditioner is efficient and robust w.r.t. the polynomial degree of the spline space. The time required for the application is almost proportional to the number of degrees-of-freedom, for a serial execution.

翻译：本文针对薛定谔方程提出一种时空最小二乘等几何离散格式，并设计参数域内线性系统的预处理器。利用基函数的张量积结构，该预处理器表示为矩阵Kronecker积之和。借助经典快速对角化方法的扩展，该预处理器的应用对样条空间的多项式阶数具有高效性与稳健性，串行执行时其计算时间与自由度数几乎呈线性增长。