A Petrov-Galerkin type method for solving Axk=b, where A is symmetric complex
A Petrov-Galerkin type method for solving Axk=b, where A is symmetric complex
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DOI：
10.1109/20.106415
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发表时间：
1990
影响因子：
2.1
通讯作者：
H. A. Vorst;J. Melissen
中科院分区：
文献类型：
--
作者：
H. A. Vorst;J. Melissen
稳态涡流方程的离散化可导致线性系统Ax=B，其中复矩阵A不是厄米特的，而是可选择对称的。在正定埃尔米特的情况下，可以定义求解该系统的迭代算法。残差向量可以通过两项递归关系相互正交，这导致了众所周知的共轭梯度（CG）方法。最后通过几个涡流算例与其它方法进行了比较，说明了该方法的有效性. >
Discretization of steady-state eddy-current equations may lead to linear system Ax=b in which the complex matrix A is not Hermitian, but may be chosen symmetric. In the positive definite Hermitian case, an iterative algorithm for solving this system can be defined. The residual vectors can be made mutually orthogonal by means of a two-term recursion relation which leads to the well-known conjugate gradient (CG) method. The proposed method is illustrated by comparing it with other methods for some eddy current examples. >