中文摘要：

等几何分析方法中为了准确描述几何形体，会出现重控制点，根据等参概念构造变量场时，重控制点上的控制变量相等，即产生一组约束方程。该文运用Lagrange乘子方法来处理等几何分析方法中的重控制点问题。以Helmholz方程为例，推导了具体的带有Lagrange乘子的等几何离散方程。圆形波导及L形波导的数值算例结果表明：这种处理方法是有效的，同时也显示出等几何分析方法的自由度少、精度高的特点。

英文摘要：

Repeated control points issue in isogeometric analysis （IGA） is encountered in some shape representations. As control variables on control points are constructed by isoparametric concept, control variables on repeated control points have the same repeated property as control points themselves. A set of constraint equations for repeated control variables are added to the functional expression with Lagrange multipliers. Take Helmholz equation for example, weakened isogeometric equations with Lagrange multipliers are formed. Circular waveguide and L-shaped waveguide are addressed as numerical examples. The results demonstrate the proposed method is effective for repeated control points issue, and also, yields more excellent results and consumes fewer amounts of DOFs than the traditional method.