Most of current corrected panel methods failed to correct out-of-phase part of distributed unsteady pressure. A method combining traditional downwash weighting method and successive kernel expansion is developed. Precision of the method is verified with an example on ONERA M6 wing. Based on modified aerodynamics,flutter boundary of wing is calculated which predicts well nonlinear flutter of wing in transonic regime.

A corrected panel method is shown and applied to static aeroealsticity.Based on CFD data at different attack angles the method approximates curved lifting lines by linear segment.The corrected panel method fills drawback of original one by considering nonlinear factor.Compared with CFD,similar accuracy limit and higher efficiency are obtained in aerodynamic force loss and attack angle compensation of M6 wing.It indicates that the method is suitable for complex structure optimization.

We propose a layer-oriented integration arithmetic for conformal perfectly matched layer (CPML).It reduces number of element and computational scale by superposing multilayer integration to monolayer integration.To retain geometrical and material information of multilayer elements we mesh CPML by multilayer elements and calculate element matrixes by monolayer integration.Numerical examples show that layer-oriented integration CPML is a reliable and high-efficient absorbing boundary condition.

Based on incomplete Cholesky decomposition with two thresholds,we propose an improved incomplete Cholesky conjugate gradient (ICCG) method with diagonal elements modification.It ensures accurate and efficient decomposition and solution of large scale sparse linear equations. The method shows advantage in computing time and storage requirment.It is applicable to solve the systems of linear equations from FEM finite element method.

By the merits of hierarchial orthogonal polynomial, a method of constructing a class of orthogonal-reinforced hierarchical hexahedra vector finite elements(ORHHVFE) to achieve a better condition of systematic matrix is presented, and the basis functions of hierarchical hexahedra vector finite elements(HHVFE) at the angle of conforming elemental systematic matrices are studied in detail. Numerical tests of the ORHHVFE constructed using 1-st Legendre polynomials based on the above method and the other HHVFE were carried out and compared. The results show that the ORHHVFE has the same numerical precision with the HHVFE, and the conditions of systematic matrices by the ORHHVFE are improved largely.