地下水流并行有限层方法及同伦反演研究

根据有限层求解格式存在的解耦性，实现了地下水三维流问题的高效并行化计算。在此基础上，结合非线性同伦方法，提出了地下水参数反演分析的并行同伦算法，利用MATLAB编译了相应的正反演计算程序。与已有解析解和有限差分解的对比以及数值算例，验证了并行化正反演方法及程序的正确性，探讨了并行算法的计算效率。研究表明，并行方法可以有效提高计算速度，较串行方法具有明显优势，同时同伦反演方法具有大范围收敛的特点，不依赖于参数值的初始选取。

Parallel finite layer method for groundwater flow and its homotopy inversion algorithm

According to the decouplization of the finite layer scheme,efficient parallel computation of the three-dimensional groundwater flow problem is presented.On this basis,and further combined with the nonlinear homotopy method,a parallelized homotopy algorithm for groundwater parameter inversion analysis is proposed.The corresponding forward and inversion compute programs are developed in MATLAB.Through the comparison of existing analytical solutions,finite difference solutions and the verification numerical examples,the validity and computational efficiency of the parallel forward and inverse methods are demonstrated.The research shows that the parallel method can effectively improve the calculation speed,and has obvious advantages over the serial method.Moreover,the homotopy parallel inversion method has the characteristics of large-scale convergence and does not depend on the initial selection of parameter values.