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Author:Markkanen, Johannes
Title:Integral equation methods for extreme materials and surfaces
Integraaliyhtälömenetelmät erikoisille materiaaleille ja pinnoille
Publication type:Licentiate thesis
Publication year:2012
Pages:vii + 24 s. + liitt. 34      Language:   eng
Department/School:Radiotieteen ja -tekniikan laitos
Main subject:Sähkömagnetiikka   (S-96)
Supervisor:Sihvola, Ari
Instructor:Ylä-Oijala, Pasi
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
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Location:P1 Ark Aalto  594   | Archive
Keywords:anisotropic media
boundary conditions
integral equation methods
electromagnetics
numerical analysis
sähkömagneettinen väliaine
reunaehdot
integraaliyhtälömenetelmät
sähkömagnetiikka
numeerinen analyysi
Abstract (eng): Various electromagnetic problems can be formulated as boundary value problems for Maxwell's equations m which the solution must satisfy both Maxwell's equations and given boundary conditions.
This thesis investigates electromagnetic properties of recently introduced DB and D'B' boundary conditions and their material realizations.
The DB boundary condition requires that normal components of the electric and magnetic flux densities vanish at the boundary, and their normal derivatives vanish at the D'B' boundary.

Computational methods, based on integral equations, for analysing electromagnetic properties of extreme boundary conditions and their material realizations have been developed.
In surface integral equation methods the boundary conditions are enforced by expanding the unknown surface current densities with proper sets of basis functions which satisfy the boundary conditions.

The realizations of the DB and D'B' boundaries require extremely anisotropic materials.
For analysing highly anisotropic media, a stable volume integral equation method is developed, and applied to study scattering properties of the realizations of the DB and D'B' boundaries.
Abstract (fin): Monet sähkömagnetiikan ongelmat voidaan muotoilla Maxwellin yhtälöiden reuna-arvo-ongelmaksi, missä ratkaisun on toteutettava sekä Maxwellin yhtälöt että jokin reunaehto.
Tässä työssä tutkitaan uusien sähkömagneettisten reunaehtojen ja näiden realisaatioiden ominaisuuksia.
Erityisesti keskitytään niin sanottuihin DB ja D'B' reunaehtoihin.
DB reunaehto vaatii sähkö- ja magneettivuontiheyksien normaalisuuntaisten komponenttien häviämisen reunalla, ja D'B' reunalla normaalikomponenttien normaaliderivaatat häviävät.

Työssä on kehitetty integraaliyhtälöihin perustuvia laskennallisia menetelmiä erikoisten reunaehtojen analysoimista varten.
Pintaintegraaliyhtälömenetelmässä reunaehdot voidaan pakottaa valitsemalla sopivat kantafunktiot, jotka toteuttavat reunaehdot.

Sekä DB että D'B'-reunaehtojen realisaatiot perustuvat väliaineisiin, jotka voivat olla voimakkaasti epäisotrooppisia.
Äärimmäisiä epäisotropioita varten työssä on kehitetty stabiili tilavuusintegraaliyhtälömenetelmä, jota on sovellettu DB ja D'B' reunaehtojen realisaatioiden tutkimuksessa.
ED:2012-05-10
INSSI record number: 44459
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