The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix.The wavelet multiresolution interpolati...The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix.The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities,including transcendental ones,in which the discretization process is as simple as that in solving linear problems,and only common two-term connection coefficients are needed.All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method,which does not require numerical integration in the resulting nonlinear discrete system.The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers.The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids,and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids.In addition,Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method,including the initial guess far from real solutions.展开更多
THE parallel strike of geochemical steep zones and geophysical gradient zones represent geochemicalboundaries with tectonic hiding and almost no magmatism, but there existed great variation of lithosphereor crustal th...THE parallel strike of geochemical steep zones and geophysical gradient zones represent geochemicalboundaries with tectonic hiding and almost no magmatism, but there existed great variation of lithosphereor crustal thickness. Tectonically, these areas were located in the foreland basins of craton margin. Thesegeochemical boundaries were usually associated with the low-temperature mineralization and petroleumgeneration. The Nd, Sr and Pb isotopic evidence indicated that there still existed strong crustal-mantle interaction through fluid activation along deep-seated faults at the craton margin. Fig. 1 is the <sup>207</sup>Pb/<sup>204</sup> Pb-<sup>208</sup>Pb/<sup>204</sup> Pb diagram, which shows the evident crust-mantle mixing for crude oil, chloroform bitumen-A,展开更多
基金supported by the National Natural Science Foundation of China(Nos.12172154 and 11925204)the 111 Project of China(No.B14044)the National Key Project of China(No.GJXM92579)。
文摘The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix.The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities,including transcendental ones,in which the discretization process is as simple as that in solving linear problems,and only common two-term connection coefficients are needed.All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method,which does not require numerical integration in the resulting nonlinear discrete system.The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers.The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids,and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids.In addition,Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method,including the initial guess far from real solutions.
文摘THE parallel strike of geochemical steep zones and geophysical gradient zones represent geochemicalboundaries with tectonic hiding and almost no magmatism, but there existed great variation of lithosphereor crustal thickness. Tectonically, these areas were located in the foreland basins of craton margin. Thesegeochemical boundaries were usually associated with the low-temperature mineralization and petroleumgeneration. The Nd, Sr and Pb isotopic evidence indicated that there still existed strong crustal-mantle interaction through fluid activation along deep-seated faults at the craton margin. Fig. 1 is the <sup>207</sup>Pb/<sup>204</sup> Pb-<sup>208</sup>Pb/<sup>204</sup> Pb diagram, which shows the evident crust-mantle mixing for crude oil, chloroform bitumen-A,
