A SPACETIME DPG METHOD FOR THE SCHRODINGER EQUATION

摘要

A spacetirne discontinuous Petrov-Calerkin (DGP) method for the linear time dependent Schri.klinger equation is proposed. The spacetime approach is particularly attractive for capturing irregular solutions. motivated by the fact that some irregular Schrodinger solutions cannot be solutions of mrtain first order reformulations, the proposed spacetime method uses the second order Schredinger operator. Two variational formulations are proved to be well posed: a strong formulation (with no relaxation of the original equation) and a weak formulation (also called the raweak formulation," which transfers all derivatives onto test functions). The convergence of the DPC met hod based on the ultrawoak formulation is investigated using an interpolation operator. A stand-alone appendix analyzes the ultraweak formulation for general differential operators. Reports of numerical experiments motivated by pulsee propagation in dispersive optical fibers are also included.