Krylov subspace exponential time domain solution of Maxwell's equations in photonic crystal modeling
نویسنده
چکیده
The exponential time integration, i.e., time integrationwhich involves thematrix exponential, is an attractive tool for time domain modeling involving Maxwell’s equations. However, its application in practice often requires a substantial knowledge of numerical linear algebra algorithms, such as Krylov subspace methods. In this note we discuss exponential Krylov subspace time integrationmethods and provide a simple guide on how to use these methods in practice. While specifically aiming at nanophotonics applications, we intentionally keep the presentation as general as possible and consider full vectorMaxwell’s equationswith damping (i.e., with nonzero conductivity terms). Efficient techniques such as the Krylov shift-and-invert method and residual-based stopping criteria are discussed in detail. Numerical experiments are presented to demonstrate the efficiency of the discussed methods and their mesh independent convergence. Some of the algorithms described here are available as Octave/Matlab codes from www.math.utwente.nl/~botchevma/expm/. © 2015 Elsevier B.V. All rights reserved.
منابع مشابه
Finite-Difference Time-Domain Simulation of Light Propagation in 2D Periodic and Quasi-Periodic Photonic Structures
Ultra-short pulse is a promising technology for achieving ultra-high data rate transmission which is required to follow the increased demand of data transport over an optical communication system. Therefore, the propagation of such type of pulses and the effects that it may suffer during its transmission through an optical waveguide has received a great deal of attention in the recent years. We...
متن کاملUnconditionally stable integration of Maxwell's equations
Numerical integration of Maxwell's equations is often based on explicit methods accepting a stability step size restriction. In literature evidence is given that there is also a need for unconditionally stable methods, as exemplified by the successful alternating direction implicitfinite difference time domain scheme. In this paper we discuss unconditionally stable integration for a general sem...
متن کاملSolution of time-convolutionary Maxwell's equations using parameter-dependent Krylov subspace reduction
We suggest a new algorithm for the solution of the time domain Maxwell equations in dispersive media. After spacial discretization we obtain a large system of time-convolution equations. Then this system is projected onto a small subspace consisting of the Laplace domain solutions for a preselected set of Laplace parameters. This approach is a generalization of the rational Krylov subspace appr...
متن کاملKrylov Subspace Approximation for TEM Simulation in the Time Domain
Forward transient electromagnetic modeling requires the numerical solution of a linear constant-coefficient initial-value problem for the quasi-static Maxwell equations. After discretization in space this problem reduces to a large system of ordinary differential equations, which is typically solved using finite-difference time-stepping. We compare standard time-stepping schemes such as the exp...
متن کاملMatrix exponential and Krylov subspaces for fast time domain computations: recent advances
By using the matrix exponential operator, solution of the system can be written as y(t) = exp(−tA)v. Numerical algorithms, which are based on this approach, are called exponential time integration methods. The essential point is that not the matrix exponential itself but rather its action on the vector v is computed. An attractive feature of the formula y(t) = exp(−tA)v is that it provides solu...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Computational Applied Mathematics
دوره 293 شماره
صفحات -
تاریخ انتشار 2016