The infinite domain potential problems arise in many branches of scientific and engineering fields, which by now still pose a great challenge to scientific computing community.This study proposes a novel meshless sing...The infinite domain potential problems arise in many branches of scientific and engineering fields, which by now still pose a great challenge to scientific computing community.This study proposes a novel meshless singular boundary method (SBM) to solve infinite domain potential problems.The SBM is mathematically simple, easy-to-program, meshless and integration-free.To guar-antee the uniqueness of numerical solutions, this article adds a constant term into the SBM approximate representation.The effi-ciency and accuracy of the proposed technique are tested to the three infinite domain potential problems.展开更多
The application of the singular boundary method(SBM),a relatively new meshless boundary collocation method,to the inverse Cauchy problem in threedimensional(3D)linear elasticity is investigated.The SBM involves a coup...The application of the singular boundary method(SBM),a relatively new meshless boundary collocation method,to the inverse Cauchy problem in threedimensional(3D)linear elasticity is investigated.The SBM involves a coupling between the non-singular boundary element method(BEM)and the method of fundamental solutions(MFS).The main idea is to fully inherit the dimensionality advantages of the BEM and the meshless and integration-free attributes of the MFS.Due to the boundary-only discretizations and its semi-analytical nature,the method can be viewed as an ideal candidate for the solution of inverse problems.The resulting ill-conditioned algebraic equations is regularized here by employing the first-order Tikhonov regularization technique,while the optimal regularization parameter is determined by the L-curve criterion.Numerical results with both smooth and piecewise smooth geometries show that accurate and stable solution can be obtained with a comparatively large level of noise added into the input data.展开更多
基金supported by the National Natural Science Foundation of China (10672051)Natural Science Foundation of Hohai University (409251)
文摘The infinite domain potential problems arise in many branches of scientific and engineering fields, which by now still pose a great challenge to scientific computing community.This study proposes a novel meshless singular boundary method (SBM) to solve infinite domain potential problems.The SBM is mathematically simple, easy-to-program, meshless and integration-free.To guar-antee the uniqueness of numerical solutions, this article adds a constant term into the SBM approximate representation.The effi-ciency and accuracy of the proposed technique are tested to the three infinite domain potential problems.
基金The work described in this paper was supported by the National Natural Science Foundation of China(Nos.11402075,11401332,71571108)Projects of International(Regional)Cooperation and Exchanges of NSFC(No.71611530712)+2 种基金the Natural Science Foundation of Shandong Province of China(Nos.ZR2017BA003,ZR2015GZ007,ZR2017JL004)the Research Grants Council of the Hong Kong Special Administrative Region(No.CityU 11204414)the Science and Technology Innovation Commission of Shenzhen Municipality(No.JCYJ20160229165310679).
文摘The application of the singular boundary method(SBM),a relatively new meshless boundary collocation method,to the inverse Cauchy problem in threedimensional(3D)linear elasticity is investigated.The SBM involves a coupling between the non-singular boundary element method(BEM)and the method of fundamental solutions(MFS).The main idea is to fully inherit the dimensionality advantages of the BEM and the meshless and integration-free attributes of the MFS.Due to the boundary-only discretizations and its semi-analytical nature,the method can be viewed as an ideal candidate for the solution of inverse problems.The resulting ill-conditioned algebraic equations is regularized here by employing the first-order Tikhonov regularization technique,while the optimal regularization parameter is determined by the L-curve criterion.Numerical results with both smooth and piecewise smooth geometries show that accurate and stable solution can be obtained with a comparatively large level of noise added into the input data.
