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Multilevel Constructions

  • The thesis consists of the two chapters. The first chapter is addressed to make a deep investigation of the MLMC method. In particular we take an optimisation view at the estimate. Rather than fixing the number of discretisation points \(n_i\) to be a geometric sequence, we are trying to find an optimal set up for \(n_i\) such that for a fixed error the estimate can be computed within a minimal time. In the second chapter we propose to enhance the MLMC estimate with the weak extrapolation technique. This technique helps to improve order of a weak convergence of a scheme and as a result reduce CC of an estimate. In particular we study high order weak extrapolation approach, which is know not be inefficient in the standard settings. However, a combination of the MLMC and the weak extrapolation yields an improvement of the MLMC.

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Author:Anton Kostiuk
URN (permanent link):urn:nbn:de:hbz:386-kluedo-39422
Advisor:Ralf Korn
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2014/12/09
Year of Publication:2014
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2014/10/13
Date of the Publication (Server):2014/12/10
Number of page:X, 103
2. Gutachter der Dissertation:

     Prof. Dr. Ömür Uğur, 
     Middle East Technical University
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 28.10.2014