Tikhonov Regularization for the Modified Mapping-collocation Method Applied to Circumferential Crack in a Curved Beam
نویسندگان
چکیده
The modified mapping-collocation (MMC) method is applied to the problem of an isotropic curved beam with a circumferential crack under pure bending moment. Using least squares method to solve the overdetermined system of boundary condition equations causes numerical difficulties. Alternatively zeroth-order Tikhonov regularization is applied to solve the system. The regularization technique appears brilliantly helpful in eliminating the convergence problems associated with ill-posedness of the problem. The boundary condition satisfaction is examined. The results of stress analysis are in good agreement with that of the finite element method.
منابع مشابه
A numerical approach for solving a nonlinear inverse diusion problem by Tikhonov regularization
In this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. In additional, the least-squares method is adopted tond the solution. To regularize the resultant ill-conditioned linear system ofequations, we apply the Tikhonov regularization method to obtain the stablenumerical approximation to the solution. Some numerical experiments con-rm the utility of th...
متن کاملروشهای تجزیه مقادیر منفرد منقطع و تیخونوف تعمیمیافته در پایدارسازی مسئله انتقال به سمت پائین
The methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. Practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. In the geoid computations witho...
متن کاملIll-Posed and Linear Inverse Problems
In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.
متن کاملAn Approximate Solution of Functionally Graded Timoshenko Beam Using B-Spline Collocation Method
Collocation methods are popular in providing numerical approximations to complicated governing equations owing to their simplicity in implementation. However, point collocation methods have limitations regarding accuracy and have been modified upon with the application of B-spline approximations. The present study reports the stress and deformation behavior of shear deformable functionally grad...
متن کاملNumerical Solution of First-kind Volterra Equations by Sequential Tikhonov Regularization
We consider the problem of finding regularized solutions to ill-posed Volterra integral equations. The method we consider is a sequential form of Tikhonov regularization that is particularly suited to problems of Volterra type. We prove that when this sequential regularization method is coupled with several standard discretizations of the integral equation (collocation, rectangular and midpoint...
متن کامل