We consider the space-time discretization of the diffusion equation, using an isogeometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) approximation in time. Drawing inspiration from a former spectral analysis, we propose for the resulting space-time linear system a multigrid preconditioned GMRES method, which combines a preconditioned GMRES with a standard multigrid acting only in space. The performance of the proposed solver is illustrated through numerical experiments, which show its competitiveness in terms of iteration count, run-time and parallel scaling.

中文翻译：

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扩散方程时空 IgA-DG 离散化的快速并行求解器

我们考虑扩散方程的时空离散化，使用空间中的等几何分析 (IgA) 近似和时间上的不连续伽辽金 (DG) 近似。从以前的光谱分析中汲取灵感，我们为由此产生的时空线性系统提出了多重网格预处理 GMRES 方法，该方法将预处理的 GMRES 与仅在空间中起作用的标准多重网格相结合。通过数值实验说明了所提出的求解器的性能，这表明了它在迭代次数、运行时间和并行缩放方面的竞争力。