Seminar za numeričku matematiku i znan. računanje

Lokacija: 
PMF Matematički odsjek, predavaonica 104
Vrijeme: 
Četvrtak, 21 Rujan, 2017 - 12:15 to 14:00

Seminar za numeričku matematiku i znan. računanje poziva članove seminara i sve zainteresirane na predavanje:

Carla Schenker, "Solution of Nonlinear Eigenvalue Problems in Electromagnetic Field Computation using Contour Integrals"

Sažetak:

Electromagnetic eigenvalue problems arising from Finite Element or Finite Integration simulations may become non-linear (in the algebraic sense) if they include certain loss mechanisms which depend on the searched eigenfrequency.

Beyn’s algorithm  (Beyn, Linear Algebra and its Applications 436:3839-3863, 2012) provides a novel method for solving such nonlinear eigenvalue problems. The algorithm uses contour integration to compute all eigenvalues inside a given closed contour in the complex plane. The main challenge is the large computational cost that arises from solving a number of shifted linear systems of equations at each integration node.

We depict the error caused by the numerical integration using an interpretation of the quadrature rule as a filter function. A significant speed up of the algorithm is achieved through a well-considered choice of contours together with quadrature rules. Using conformal mapping techniques the performance near points of non-holomorphicity can be drastically improved (Barel, Kravanja, Journal of computational and applied mathematics 292(1):526-540, 2016).

Convergence results are demonstrated for a model of a waveguide-coupled cavity discretised with the Finite Integration Technique (FIT). The choices of parameters within the algorithm are discussed as well as further improvements.

Lijep pozdrav,

                                        Tina Bosner

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