Space-time least squares approximation for Schr\"odinger equation and efficient solver
CoRR(2023)
摘要
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.
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