In this work, by choosing an orthonormal basis for the Hilbert space L^2[0, 1], an approximation method for finding approximate solutions of the equation （I ＋ K）x = y is proposed, called Haar wavelet approximation ...In this work, by choosing an orthonormal basis for the Hilbert space L^2[0, 1], an approximation method for finding approximate solutions of the equation （I ＋ K）x = y is proposed, called Haar wavelet approximation method （HWAM）. To prove the applicabifity of the HWAM, a more general applicability theorem on an approximation method （AM） for an operator equation Ax = y is proved first. As an application, applicability of the HWAM is obtained. Fhrthermore, four steps to use the HWAM are listed and three numerical examples are given in order to illustrate the effectiveness of the method.展开更多
We consider the approximate acoustic cloaking in an inhomogeneous isotropic background space.By employing transformation media,together with the use of a sound-soft layer lining right outside the cloaked region,we sho...We consider the approximate acoustic cloaking in an inhomogeneous isotropic background space.By employing transformation media,together with the use of a sound-soft layer lining right outside the cloaked region,we show that one can achieve the near-invisibility by the"blow-up-a-small-region"construction.This is based on novel scattering estimates corresponding to multiple multi-scale obstacles located in an isotropic space.We develop a novel system of integral equations to decouple the nonlinear scattering interaction among the small obstacle components,the regular obstacle components and the inhomogeneous background medium.展开更多
基金support by the NSFC(11371012,11401359,11471200)the FRF for the Central Universities(GK201301007)the NSRP of Shaanxi Province(2014JQ1010)
文摘In this work, by choosing an orthonormal basis for the Hilbert space L^2[0, 1], an approximation method for finding approximate solutions of the equation （I ＋ K）x = y is proposed, called Haar wavelet approximation method （HWAM）. To prove the applicabifity of the HWAM, a more general applicability theorem on an approximation method （AM） for an operator equation Ax = y is proved first. As an application, applicability of the HWAM is obtained. Fhrthermore, four steps to use the HWAM are listed and three numerical examples are given in order to illustrate the effectiveness of the method.
基金supported by National Natural Science Foundation of China(Grant Nos.1110141411201453+1 种基金91130022 and 91130026)National Science Foundation of USA(Grant No.DMS 1207784)
文摘We consider the approximate acoustic cloaking in an inhomogeneous isotropic background space.By employing transformation media,together with the use of a sound-soft layer lining right outside the cloaked region,we show that one can achieve the near-invisibility by the"blow-up-a-small-region"construction.This is based on novel scattering estimates corresponding to multiple multi-scale obstacles located in an isotropic space.We develop a novel system of integral equations to decouple the nonlinear scattering interaction among the small obstacle components,the regular obstacle components and the inhomogeneous background medium.
