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Author: | Leinonen, Matti |
Title: | Stochastic Galerkin Finite Element Method with Log-normal Random Field |
Stokastinen Galerkinin elementtimenetelmä log-normaalin satunnaiskentän tapauksessa | |
Publication type: | Master's thesis |
Publication year: | 2011 |
Pages: | [5] + 58 Language: eng |
Department/School: | Matematiikan ja systeemianalyysin laitos |
Main subject: | Matematiikka (Mat-1) |
Supervisor: | Nevanlinna, Olavi |
Instructor: | Hakula, Harri ; Hyvönen, Nuutti |
Electronic version URL: | http://urn.fi/URN:NBN:fi:aalto-201207022736 |
OEVS: | Electronic archive copy is available via Aalto Thesis Database.
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Location: | P1 Ark Aalto 219 | Archive |
Keywords: | stochastic Galerkin finite element method polynomical chaos Karhunen-Loéve expansion log-normal distribution random field sGFEM sFEM stokastinen Galerkinin elementtimenetelmä polynomikaaos Karhunen-Loéve-hajotelma log-normaalijakauma satunnaiskenttä sGFEM sFEM |
Abstract (eng): | Stochastic Galerkin finite element method (sGFEM) is introduced together with the associated mathematical tools, and implemented for a one-dimensional stochastic linear elliptic boundary value problem that can be considered as the stochastic conductivity equation reduced to one dimension. The conductivity coefficient of the model problem is assumed to be a log-normal random field with a known mean field and covariance function. The contact impedances of the model are assumed to be known log-normal random variables. According to numerical tests, the sGFEM is found to be a feasible choice when the variances of the stochastic parameters are not huge. |
Abstract (fin): | Työssä esitellään stokastinen Galerkinin elementtimenetelmä (sGFEM) yhdessä tarvittavien matemaattisten työkalujen kanssa. Menetelmä toteutetaan yksiulotteiselle stokastiselle lineaariselle elliptiselle reuna-arvo-ongelmalle, jonka voidaan ajatella kuvaavan stokastista johtavuusyhtälöä yhdessä ulottuvuudessa. Malliongelman johtavuuskertoimen oletetaan olevan log-normaali satunnaiskenttä tunnetulla odotusarvolla ja kovarianssifunktiolla. Mallin kontakti-impedanssien oletetaan olevan tunnettuja log-normaaleja satunnaismuuttujia. Numeeristen kokeiden perusteella menetelmän todetaan toimivan, jos parametrien varianssit eivät ole liian suuria. |
ED: | 2011-12-21 |
INSSI record number: 43643
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