Convergence of Hardy Space Infinite Elements for Helmholtz Scattering and Resonance Problems
نویسنده
چکیده
We perform a convergence analysis for discretization of Helmholtz scattering and resonance problems obtained by Hardy space infinite elements. Super-algebraic convergence with respect to the number of Hardy space degrees of freedom is achieved. As transparent boundary spheres and piecewise polytopes are considered. The analysis is based on a G̊arding-type inequality and standard operator theoretical results.
منابع مشابه
High order Curl-conforming Hardy space infinite elements for exterior Maxwell problems
A construction of prismatic Hardy space infinite elements to discretize wave equations on unbounded domains Ω in H loc(Ω), Hloc(curl; Ω) and Hloc(div; Ω) is presented. As our motivation is to solve Maxwell’s equations we take care that these infinite elements fit into the discrete de Rham diagram, i.e. they span discrete spaces, which together with the exterior derivative form an exact sequence...
متن کاملThe computation of resonances in open systems using a perfectly matched layer
In this paper, we consider the problem of computing resonances in open systems. We first characterize resonances in terms of (improper) eigenfunctions of the Helmholtz operator on an unbounded domain. The perfectly matched layer (PML) technique has been successfully applied to the computation of scattering problems. We shall see that the application of PML converts the resonance problem to a st...
متن کاملAn efficient method for the numerical solution of Helmholtz type general two point boundary value problems in ODEs
In this article, we propose and analyze a computational method for numerical solution of general two point boundary value problems. Method is tested on problems to ensure the computational eciency. We have compared numerical results with results obtained by other method in literature. We conclude that propose method is computationally ecient and eective.
متن کاملA coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator
The Helmholtz equation governing wave propagation and scattering phenomena is difficult to solve numerically. Its discretization with piecewise linear finite elements results in typically large linear systems of equations. The inherently parallel domain decomposition methods constitute hence a promising class of preconditioners. An essential element of these methods is a good coarse space. Here...
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:
- SIAM J. Numerical Analysis
دوره 54 شماره
صفحات -
تاریخ انتشار 2016