کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
522070 867809 2008 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Dispersive properties of multisymplectic integrators
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Dispersive properties of multisymplectic integrators
چکیده انگلیسی

Multisymplectic (MS) integrators, i.e. numerical schemes which exactly preserve a discrete space–time symplectic structure, are a new class of structure preserving algorithms for solving Hamiltonian PDEs. In this paper we examine the dispersive properties of MS integrators for the linear wave and sine-Gordon equations. In particular a leapfrog in space and time scheme (a member of the Lobatto Runge–Kutta family of methods) and the Preissman box scheme are considered. We find the numerical dispersion relations are monotonic and that the sign of the group velocity is preserved. The group velocity dispersion (GVD) is found to provide significant information and succinctly explain the qualitative differences in the numerical solutions obtained with the different schemes. Further, the numerical dispersion relations for the linearized sine-Gordon equation provides information on the ability of the MS integrators to capture the sine-Gordon dynamics. We are able to link the numerical dispersion relations to the total energy of the various methods, thus providing information on the coarse grid behavior of MS integrators in the nonlinear regime.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 227, Issue 10, 1 May 2008, Pages 5090–5104
نویسندگان
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