Search results for "raja-arvo"
showing 3 items of 3 documents
Electromagnetic wave propagation in non-homogeneous waveguides
2015
We investigate an electromagnetic waveguide, having several cylindrical ends. The waveguide is assumed to be empty and to have a perfectly conductive boundary. We study the electromagnetic field, excited in the waveguide in the presence of charges and currents. The field can be described as a solution of the stationary Maxwell system with conductive boundary conditions and “intrinsic” radiation conditions at infinity. We prove the problem to be well-posed. Electromagnetic waves propagation in the waveguide can be described by means of a scattering matrix. We introduce such a matrix for all values of the spectral parameter k in the waveguide continuous spectrum and study its properties. Moreove…
Shape sensitivity analysis for numerical solution of free boundary problems
2005
Kari Kärkkäinen tutki tehokkaita ja käyttökelpoisia ratkaisumenetelmiä vapaita pintoja sisältäville malleille. Hän tarkastelee väitöksessään numeerisessa simuloinnissa käytettävien vapaan pinnan ratkaisumenetelmien tehokkuutta ja niiden parantamista käyttäen matemaattista lähestymistapaa. Kärkkäinen ehdottaa ratkaisumenetelmää, jonka avulla vapaan pinnan tehtävien ratkaiseminen on helpompaa. Menetelmää voi myös soveltaa erilaisiin tilanteisiin. This work is devoted to the development of efficient and robust solution algorithms for a class of free boundary problems. This consists of mathematical analysis of different model problems and the description of numerical implementation to generic f…
Generalized wave propagation problems and discrete exterior calculus
2018
We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulat…