کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5776050 | 1631961 | 2018 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map
ترجمه فارسی عنوان
محاسبات رزونانس کارآمد برای مشکلات هلمولتز بر اساس نقشه دیریکلت تا نویمان
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
چکیده انگلیسی
We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of a Dirichlet-to-Neumann map, which accounts for modeling unbounded domains. We consider a variational formulation and show that the spectrum consists of isolated eigenvalues of finite multiplicity that only can accumulate at infinity. The proposed method is based on a high order finite element discretization combined with a specialization of the Tensor Infinite Arnoldi method (TIAR). Using Toeplitz matrices, we show how to specialize this method to our specific structure. In particular we introduce a pole cancellation technique in order to increase the radius of convergence for computation of eigenvalues that lie close to the poles of the matrix-valued function. The solution scheme can be applied to multiple resonators with a varying refractive index that is not necessarily piecewise constant. We present two test cases to show stability, performance and numerical accuracy of the method. In particular the use of a high order finite element discretization together with TIAR results in an efficient and reliable method to compute resonances.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 330, 1 March 2018, Pages 177-192
Journal: Journal of Computational and Applied Mathematics - Volume 330, 1 March 2018, Pages 177-192
نویسندگان
Juan Carlos Araujo-Cabarcas, Christian Engström, Elias Jarlebring,