Sökning: onr:"swepub:oai:DiVA.org:kth-216793" >
Efficient resonance...
Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map
-
- Araujo-Cabarcas, Juan Carlos (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå university, Sweden
-
- Engström, Christian (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Umeå university, Sweden
-
- Jarlebring, Elias (författare)
- KTH,SeRC - Swedish e-Science Research Centre,Matematik (Inst.),KTH Royal Instute of Technology, Sweden
-
(creator_code:org_t)
- Amsterdam : Elsevier, 2018
- 2018
- Engelska.
-
Ingår i: Journal of Computational and Applied Mathematics. - Amsterdam : Elsevier. - 0377-0427 .- 1879-1778. ; 330, s. 177-192
- Relaterad länk:
-
https://doi.org/10.1...
-
visa fler...
-
https://urn.kb.se/re...
-
https://doi.org/10.1...
-
https://urn.kb.se/re...
-
https://urn.kb.se/re...
-
visa färre...
Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Arnoldi's method
- Dirichlet-to-Neumann map
- Helmholtz problem
- Matrix functions
- Nonlinear eigenvalue problems
- Scattering resonances
- Finite element method
- Matrix algebra
- Numerical methods
- Poles
- Refractive index
- Resonance
- Switching systems
- Arnoldi's methods
- Helmholtz problems
- Nonlinear eigenvalue problem
- Scattering resonance
- Eigenvalues and eigenfunctions
- Mathematics
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
Hitta via bibliotek
Till lärosätets databas