Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Sparse second moment analysis for elliptic problems in stochastic domains

by R. Harbrecht and R Schneider and Ch. Schwab

(Report number 2007-02)

Abstract
We consider the numerical solution of elliptic boundary value problems in domains with random boundary perturbations. Assuming normal perturbations with small amplitude and known mean field and two-point correlation function, we derive, using a second order shape calculus, deterministic equations for the mean field and the two-point correlation function of the random solution for a model Dirichlet problem which are 3rd order accurate in the boundary perturbation size. Using a variational boundary integral equation formulation on the unperturbed, "nominal" boundary and a wavelet discretization, we present and analyze an algorithm to approximate the random solution's mean and its two-point correlation function at essentially optimal order in essentially O(N) work and memory, where N denotes the number of unknowns required for consistent discretization of the boundary of the nominal domain.

Keywords:

@Techreport{HSS07_363,
  author = {R. Harbrecht and R Schneider and Ch. Schwab},
  title = {Sparse second moment analysis for elliptic problems in stochastic domains},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2007-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2007/2007-02.pdf },
  year = {2007}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).