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DOI: 10.5445/IR/1000086907
Veröffentlicht am 24.10.2018

Improved efficiency of a multi-index FEM for computational uncertainty quantification

Dick, Josef; Feischl, Michael; Schwab, Christoph

Abstract:
We propose a multi-index algorithm for the Monte Carlo discretization of a linear, elliptic PDE with affine-parametric input. We prove an error vs. work analysis which allows a multi-level finite-element approximation in the physical domain, and apply the multi-index analysis with isotropic, unstructured mesh refinement in the physical domain for the solution of the forward problem, for the approximation of the random field, and for the Monte-Carlo quadrature error. Our approach allows general spatial domains and unstructured mesh hierarchies. The improvement in complexity is obtained from combining spacial discretization, dimension truncation and MC sampling in a multi-index fashion. Our analysis improves cost estimates compared to multi-level algorithms for similar problems and mathematically underpins the outstanding practical performance of multi-index algorithms for partial differential equations with random coefficients.


Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
URN: urn:nbn:de:swb:90-869076
KITopen ID: 1000086907
Verlag KIT, Karlsruhe
Umfang 20 S.
Serie CRC 1173 ; 2018/22
Schlagworte multi-index, Monte Carlo, high-dimensional, uncertainty quantification
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