کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
513216 866458 2011 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Regularized solutions with a singular point for the inverse biharmonic boundary value problem by the method of fundamental solutions
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Regularized solutions with a singular point for the inverse biharmonic boundary value problem by the method of fundamental solutions
چکیده انگلیسی

Two numerical methods for the Cauchy problem of the biharmonic equation are proposed. The solution of the problem does not continuously depend on given Cauchy data since the problem is ill-posed. A small noise contained in the Cauchy data sensitively affects on the accuracy of the solution. Our problem is directly discretized by the method of fundamental solutions (MFS) to derive an ill-conditioned matrix equation. As another method, our problem is decomposed into two Cauchy problems of the Laplace and the Poisson equations, which are discretized by the MFS and the method of particular solutions (MPS), respectively. The Tikhonov regularization and the truncated singular value decomposition are applied to the matrix equation to stabilize a numerical solution of the problem for the given Cauchy data with high noises. The L-curve and the generalized cross-validation determine a suitable regularization parameter for obtaining an accurate solution. Based on numerical experiments, it is concluded that the numerical method proposed in this paper is effective for the problem that has an irregular domain and the Cauchy data with high noises. Furthermore, our latter method can successfully solve the problem whose solution has a singular point outside the computational domain.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Engineering Analysis with Boundary Elements - Volume 35, Issue 7, July 2011, Pages 883–894
نویسندگان
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