On Magnus Integrators for Time-Dependent Schrödinger Equations

نویسندگان

  • Marlis Hochbruck
  • Christian Lubich
چکیده

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Towards an Adaptive Solver for High-Dimensional PDE Problems on Clusters of Multicore Processors

Accurate numerical simulation of time-dependent phenomena in many spatial dimensions is a challenging computational task apparent in a vast range of application areas, for instance quantum dynamics, financial mathematics, systems biology and plasma physics. Particularly problematic is that the number of unknowns in the governing equations (the number of grid points) grows exponentially with the...

متن کامل

High-order commutator-free Magnus integrators and related methods for non-autonomous linear evolution equations

The class of commutator-free Magnus integrators is known to provide a favourable alternative to standard Magnus integrators, in particular for large-scale applications arising in the time integration of non-autonomous linear evolution equations. A high-order commutator-free Magnus integrator is given by a composition of several exponentials that comprise certain linear combinations of the value...

متن کامل

A Local Strong form Meshless Method for Solving 2D time-Dependent Schrödinger Equations

This paper deals with the numerical solutions of the 2D time dependent Schr¨odinger equations by using a local strong form meshless method. The time variable is discretized by a finite difference scheme. Then, in the resultant elliptic type PDEs, special variable is discretized with a local radial basis function (RBF) methods for which the PDE operator is also imposed in the local matrices. Des...

متن کامل

The solution of stationary ODE problems in quantum mechanics by Magnus methods with stepsize control

In solid state physics the solution of the Dirac and Schrödinger equation by operator splitting methods leads to differential equations with oscillating solutions for the radial direction. For standard time integrators like Runge–Kutta or multistep methods the stepsize is restricted approximately by the length of the period. In contrast the recently developed Magnus methods allow stepsizes that...

متن کامل

Parallel-in-time Magnus Integrators

Magnus integrators are a subset of geometric integration methods for the numerical solution of ordinary differential equations that conserve certain invariants in the numerical solution. This paper explores temporal parallelism of Magnus integrators, particularly in the context of nonlinear problems. The approach combines the concurrent computation of matrix commutators and exponentials within ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • SIAM J. Numerical Analysis

دوره 41  شماره 

صفحات  -

تاریخ انتشار 2003