Integral equation methods for extreme-parameter materials and novel boundary conditions

Johannes Markkanen

Integral equation methods for extreme-parameter materials and novel boundary conditions

Julkaisun otsikon käännös: Integraaliyhtälömenetelmät äärimmäisille materiaaleille ja uusille reunaehdoille

Johannes Markkanen

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Väitöskirjan tavoitteena on kehittää tarkkoja ja tehokkaita numeerisia menetelmiä mallintamaan materiaalien sähkömagneettisia ominaisuuksia. Työssä tutkitaan materiaaleja, joiden sähkömagneettista vastetta kuvaavat parametrit permittiivisyys ja permeabiilisuus voivat olla voimakkaasti riippuvaisia kentän suunnasta tai saada äärimmäisiä arvoja. Lisäksi työssä tutkitaan erikoisia niin sanottuja DB ja D'B' reunaehtoja, jotka rajoittavat kenttien normaalikomponenttien tai niiden normaali derivaattojen käyttäytymistä. Väitöskirja voidaan karkeasti jakaa kolmeen osaan. Ensimmäisessä osassa kehitetään pintaintegraaliyhtälöihin perustuvia laskennallisia menetelmiä sähkömagneettisten sirontaongelmien ratkaisemiseksi kappaleista, joiden pinnalla DB reunaehto on voimassa. Menetelmässä DB reunaehto pakotetaan voimaan rajoittamalla tuntemattomien pintavirtatiheyksien käyttäytymistä kappaleen pinnalla. Lisäksi tutkitaan DB kappaleiden sähkömagneettisia sirontaominaisuuksia. Toisessa osassa tarkastellaan tilavuusintegraaliyhtälömenetelmien ominaisuuksia. Erityisesti perehdytään diskretoitujen yhtälöiden tarkkuuteen ja stabiilisuuteen kun materiaaliparametrit lähestyvät äärimmäisiä arvoja. Työssä näytetään että tilavuusvirtoihin perustuva formulaatio käyttäytyy paremmin kuin tavanomaiset formulaatiot kun materiaaliparametrit ovat voimakkaasti epäsotrooppisia. Lopuksi väitöskirja käsittelee DB ja D'B' reunaehtojen realisointia sähkömagneettisten materiaaliparametrien avulla. Realisaatiot vaativat voimakkaasti epäisotrooppisia materiaaleja, joiden laskennalliseen mallintamiseen käytetään toisessa osassa kehitettyä menetelmää.

Julkaisun otsikon käännös	Integraaliyhtälömenetelmät äärimmäisille materiaaleille ja uusille reunaehdoille
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Sihvola, Ari, Vastuuprofessori Ylä-Oijala, Pasi, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-60-5242-7
Sähköinen ISBN	978-952-60-5243-4
Tila	Julkaistu - 2013
OKM-julkaisutyyppi	G5 Tohtorinväitöskirja (artikkeli)

Tutkimusalat

integraaliyhtälömenetelmät
momenttimenetelmä
DB reunaehto
D'B' reunaehto
anisotropia
äärimmäiset materiaalit

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-60-5243-4

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@phdthesis{3204d825fcb44b2fa1d81a473e7c5629,

title = "Integral equation methods for extreme-parameter materials and novel boundary conditions",

abstract = "This thesis aims to develop accurate and efficient numerical methods for modeling electromagnetic properties of materials with extreme parameters and nonconventional boundary conditions. Materials with the permittivity and permeability dyadics being strongly inhomogeneous or anisotropic or having parameters near zero or infinity are considered as extreme materials. Nonconventional boundary conditions investigated in this thesis are called DB and D'B' boundary conditions, which require the vanishing of the normal components of the fluxes (DB) or their normal derivatives (D'B'). This thesis consists of three main topics. In the first part, a surface integral equation-based solution for electromagnetic wave scattering by objects with the DB boundary condition is developed. The integral equations are solved by the method of moments. The DB boundary condition is enforced by restricting the freedom of the unknown surface current densities. The developed method is then used for analyzing electromagnetic scattering by the ideal DB objects. The second part examines properties of different volume integral equation formulations and their discretizations. The accuracy and stability of these formulations are analyzed when the material parameters are complicated or pushed to the extreme limits. It is shown that the formulation with the equivalent volume currents as unknowns is more stable than the conventional ones when the material parameters are extremely anisotropic. The third part focuses on material approximations of the DB and D'B' boundary conditions in terms of an interface against some extreme-parameter material. Scattering properties of these approximations are investigated by using the volume integral equation method developed in the second part.",

keywords = "integral equation methods, method of moments, DB boundary condition, D'B' boundary condition, anisotropy, extreme materials, integraaliyht{\"a}l{\"o}menetelm{\"a}t, momenttimenetelm{\"a}, DB reunaehto, D'B' reunaehto, anisotropia, {\"a}{\"a}rimm{\"a}iset materiaalit, integral equation methods, method of moments, DB boundary condition, D'B' boundary condition, anisotropy, extreme materials",

author = "Johannes Markkanen",

year = "2013",

language = "English",

isbn = "978-952-60-5242-7",

series = "Aalto University publication series DOCTORAL DISSERTATIONS",

publisher = "Aalto University",

number = "109",

school = "Aalto University",

}

TY - THES

T1 - Integral equation methods for extreme-parameter materials and novel boundary conditions

AU - Markkanen, Johannes

PY - 2013

Y1 - 2013

N2 - This thesis aims to develop accurate and efficient numerical methods for modeling electromagnetic properties of materials with extreme parameters and nonconventional boundary conditions. Materials with the permittivity and permeability dyadics being strongly inhomogeneous or anisotropic or having parameters near zero or infinity are considered as extreme materials. Nonconventional boundary conditions investigated in this thesis are called DB and D'B' boundary conditions, which require the vanishing of the normal components of the fluxes (DB) or their normal derivatives (D'B'). This thesis consists of three main topics. In the first part, a surface integral equation-based solution for electromagnetic wave scattering by objects with the DB boundary condition is developed. The integral equations are solved by the method of moments. The DB boundary condition is enforced by restricting the freedom of the unknown surface current densities. The developed method is then used for analyzing electromagnetic scattering by the ideal DB objects. The second part examines properties of different volume integral equation formulations and their discretizations. The accuracy and stability of these formulations are analyzed when the material parameters are complicated or pushed to the extreme limits. It is shown that the formulation with the equivalent volume currents as unknowns is more stable than the conventional ones when the material parameters are extremely anisotropic. The third part focuses on material approximations of the DB and D'B' boundary conditions in terms of an interface against some extreme-parameter material. Scattering properties of these approximations are investigated by using the volume integral equation method developed in the second part.

AB - This thesis aims to develop accurate and efficient numerical methods for modeling electromagnetic properties of materials with extreme parameters and nonconventional boundary conditions. Materials with the permittivity and permeability dyadics being strongly inhomogeneous or anisotropic or having parameters near zero or infinity are considered as extreme materials. Nonconventional boundary conditions investigated in this thesis are called DB and D'B' boundary conditions, which require the vanishing of the normal components of the fluxes (DB) or their normal derivatives (D'B'). This thesis consists of three main topics. In the first part, a surface integral equation-based solution for electromagnetic wave scattering by objects with the DB boundary condition is developed. The integral equations are solved by the method of moments. The DB boundary condition is enforced by restricting the freedom of the unknown surface current densities. The developed method is then used for analyzing electromagnetic scattering by the ideal DB objects. The second part examines properties of different volume integral equation formulations and their discretizations. The accuracy and stability of these formulations are analyzed when the material parameters are complicated or pushed to the extreme limits. It is shown that the formulation with the equivalent volume currents as unknowns is more stable than the conventional ones when the material parameters are extremely anisotropic. The third part focuses on material approximations of the DB and D'B' boundary conditions in terms of an interface against some extreme-parameter material. Scattering properties of these approximations are investigated by using the volume integral equation method developed in the second part.

KW - integral equation methods

KW - method of moments

KW - DB boundary condition

KW - D'B' boundary condition

KW - anisotropy

KW - extreme materials

KW - integraaliyhtälömenetelmät

KW - momenttimenetelmä

KW - DB reunaehto

KW - D'B' reunaehto

KW - anisotropia

KW - äärimmäiset materiaalit

KW - integral equation methods

KW - method of moments

KW - DB boundary condition

KW - D'B' boundary condition

KW - anisotropy

KW - extreme materials

M3 - Doctoral Thesis

SN - 978-952-60-5242-7

T3 - Aalto University publication series DOCTORAL DISSERTATIONS

PB - Aalto University

ER -

Integral equation methods for extreme-parameter materials and novel boundary conditions

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