Based on the symmetric-triangular (ST) decomposition technique, a class of block ST (BST) preconditioners are proposed for generalized saddle point linear systems arising from the meshfree discretization of piezoelectric equations. By applying the BST preconditioners, we first transform the generalized saddle point linear systems into symmetric positive definite ones, which then can be solved in a fast and efficient way by the classical conjugate gradient (CG) or the preconditioned CG (PCG) iteration methods. Two practical BST preconditioners are presented and analyzed in detail. Eigen-properties and upper bounds of the condition numbers of the preconditioned matrices are proved. Implementation aspects are discussed. Finally, two numerical experiments arising from the piezoelectric strip shear deformation problem and the piezoelectric strip bending problem are presented. Numerical results show that the iteration steps of the PCG methods are independent of the number of degrees of freedom and the proposed BST preconditioners perform much better than some existing preconditioning techniques.

基于对称三角形（ST）分解技术，针对压电方程的无网格离散化产生的广义鞍点线性系统，提出了一类块ST（BST）预条件子。通过应用 BST 预处理器，我们首先将广义鞍点线性系统转换为对称正定系统，然后可以通过经典共轭梯度 (CG) 或预条件 CG (PCG) 迭代方法快速有效地求解。介绍并详细分析了两个实用的 BST 预处理器。证明了预处理矩阵的本征性质和条件数的上界。讨论了实施方面。最后，提出了由压电带剪切变形问题和压电带弯曲问题引起的两个数值实验。数值结果表明，PCG 方法的迭代步骤与自由度的数量无关，并且所提出的 BST 预处理器的性能比一些现有的预处理技术要好得多。