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 p-version BEM for first kind boundary integral equations with random loading

by A. Chernov and Ch. Schwab

(Report number 2008-02)

Abstract
We consider the weakly singular boundary integral equation Vu = g(w) on a deterministic smooth closed curve T>R2 with random loading g(w). The statistical moments of g up to order k are assumed to be known. The aim is the efficient deterministic computation of statistical moments MkU:=E, k>1. We derive a deterministic formulation for the kth statistical moment. It is posed in the tensor product Sobolev space and involves the k-fold tensor product operator V(k):=V. The standard full tensor product Galerkin BEM requires O(Nk) unknowns for the kth moment problem, where N is the number of unknowns needed to discretize T. Extending ideas of (?), we develop the p-sparse grid Galerkin BEM to reduce the number of unknowns from O(Nk) to O(N(logN)k-1).

Keywords:

@Techreport{CS08_368,
  author = {A. Chernov and Ch. Schwab},
  title = {Sparse p-version BEM for first kind boundary integral equations with random loading},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-02.pdf },
  year = {2008}
}

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).