基于吸收边界条件的有限元方法和离散切比雪夫展开的二维缺陷识别

结合考虑了吸收边界条件的有限元正演方法，通过离散切比雪夫多项式在特定离散点的展开逼近待识别函数，实现了无限区域内二维缺陷的识别。正问题计算中引入的吸收边界条件虽然不能严格地模拟无限域对近场波动的影响，但能够以满足实际需要的精度模拟这一影响，且具有解耦特性，极大地简化了数值计算，在反演计算中，离散点取在切比雪夫多项式的零点处，使逼近时最大偏差最小，数值算例表明此方法的有效性。

FEM with absorbing boundary condition and expansion of discrete Chebyshev polynomials for inverse problem of elastic waves

Research of wave motion is important both in theory and application.In this paper,it discusses an identification method of two-dimensional defect.With the combination of FEM considering absorbing boundary condition for direct problem and the expansion of discrete Chebyshev polynomials at special chosen points,the identification of two-dimensional defect in infinite area is discussed. The absorbing boundary condition is obtained through approximating the Sommerfeld radiation condition.Although the absorbing boundary condition can't simulate the effect exactly,it can satisfy the approximation in practice and has the character of solving the coupling that simplifies the calculations.Because of the use of finite element method,the direct problems that involve special geometrical shaped scattering and multi-scattering can be solved.The finite element model is used iteratively to compute the scattered field.The special points are chosen at the zeros of the Chebyshev polynomials that can achieve accuracy comparable to the general expansion with fewer terms.The numerical simulation examples show the validity of this method.