کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
802149 1467872 2014 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Stability of Karhunen–Loève expansion for the simulation of Gaussian stochastic fields using Galerkin scheme
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی مکانیک
پیش نمایش صفحه اول مقاله
Stability of Karhunen–Loève expansion for the simulation of Gaussian stochastic fields using Galerkin scheme
چکیده انگلیسی


• The positive definiteness of truncated covariance function is examined.
• It is shown that truncated covariance function is not positive definite.
• A guideline to avoid numerical stability problems is proposed.
• Two numerically more efficient modifications of covariance function are proposed.

The paper investigates the problem of numerical stability of the Karhunen–Loève expansion for the simulation of Gaussian stochastic fields using Galerkin scheme. The instability is expressed as loss of positive definiteness of covariance matrix and is the result of modifications of standard exponential covariance functions that are commonly applied to increase the sparsity of the covariance matrix. The loss of positive definiteness of covariance matrix limits the use of efficient eigenvalue solvers that are needed for the solution of the resulting generalized eigenvalue problem. Two modifications of the shape of covariance function to avoid instability problems and at the same time to raise the numerical efficiency of Karhunen–Loève expansion by increasing the sparsity of the covariance matrix are proposed. The effects of the proposed modifications are demonstrated on numerical examples.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Probabilistic Engineering Mechanics - Volume 37, July 2014, Pages 7–15
نویسندگان
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