We show that the discrete operator stemming from time-space discretization of evolutionary partial differential equations can be represented in terms of a single Sylvester matrix equation. A novel solution strategy that combines projection techniques with the full exploitation of the entry-wise structure of the involved coefficient matrices is proposed. The resulting scheme is able to efficiently solve problems with a tremendous number of degrees of freedom while maintaining a low storage demand as illustrated in several numerical examples.

中文翻译：

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某些演化偏微分方程的矩阵方程技术

我们表明，源自演化偏微分方程的时空离散化的离散算子可以用单个Sylvester矩阵方程表示。提出了一种将投影技术与所涉及的系数矩阵的逐项结构的充分利用相结合的新颖解决方案策略。如几个数值示例所示，所得方案能够以极大的自由度有效解决问题，同时保持较低的存储需求。