地下水渗流的边界元非重叠区域分解算法

Boundary Element Method with Non-overlapping Domain Decomposition for Groudwater Seepage Equation

用Green公式和基本解推导得出直接边界积分方程来求解渗流问题.经边界元离散后,通过求解线性方程组和计算解的离散积分表达式得原问题的数值解.区域分解算法将大型问题分解为小型问题﹑复杂边值问题分解为简单边值问题﹑允许并行计算,此方法愈来愈受到重视.而非重叠性区域分解算法的优点是仅在边界上交换数据,避免了重叠性区域分解算法必须在公共区域计算若干公共点的值,减少了计算量,与直接边界元方法得到边界物理量可以很好配合.这两种算法结合起来求解渗流问题,而且在多个区域中可以并行计算各向异性的问题,数值算例表明该方法是有效可行的.

The direct boundary integral equation deduced by Green’s formula and the fundamental solu‐tion is considered to solve seepage problem .After the boundary is discrete ,the numerical solution is gained by solving linear equations and by calculating the discrete integration expression of solution . This paper presents the analytical formula and Gaussian quadrature to calculate the integration formu‐la .A non‐overlapping domain decomposition method combining direct boundary element formulation is applied to solve seepage problems ,and calculating orthotropic case in several domains .Constant el‐ement is used in the computing program of this paper ,which is written by Fortran90 .The numerical experiments demonstrated that the method is reliable and effective .