Abstract Single domain spectral/pseudospectral integration preconditioning matrices have been shown to be effective operators for solving differential equations. In this study we extend the integration precondition methodology to a multidomain computational framework, and construct global inverse matrices for the advection operator discretized by multidomain Gauss-Lobatto-Legendre pseudospectral methods. These inverse operators can be used as solution operators for solving first order boundary value problems even with piecewise continuous variable coefficients. Moreover, they are effective integration preconditioning matrices for the second order diffusion operator, in the sense that a model diffusion problem can be solved by an iterative method with the number of iteration steps being proportional to the number of subdomains but independent of the degree of the solution polynomial. Numerical experiments were conducted and we observed the performance of the inverse operators as expected.

中文翻译：

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对流和扩散算子的多域伪谱积分预处理矩阵

摘要 单域谱/伪谱积分预处理矩阵已被证明是求解微分方程的有效算子。在这项研究中，我们将积分前提条件方法扩展到多域计算框架，并为由多域 Gauss-Lobatto-Legendre 伪谱方法离散的对流算子构建全局逆矩阵。这些逆算子可以用作求解算子，用于求解一阶边值问题，即使是分段连续可变系数。此外，它们是二阶扩散算子的有效积分预处理矩阵，从某种意义上说，模型扩散问题可以通过迭代方法解决，迭代步骤的数量与子域的数量成正比，但与解多项式的次数无关。进行了数值实验，我们按预期观察了逆算子的性能。