High-order ADI schemes for diffusion equations with mixed derivatives in the combination technique
High-order ADI schemes for diffusion equations with mixed derivatives in the combination technique
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组合技术中具有混合导数的扩散方程的高阶 ADI 格式
DOI：
10.1016/j.apnum.2015.11.003
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
M. Günther
中科院分区：
文献类型：
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作者：
Christian Hendricks;Matthias Ehrhardt;M. Günther
在本文中，我们将稀疏网格上的高阶 (HO) 和交替方向隐式 (ADI) 方案的思想结合起来，用于具有混合导数的扩散方程。借助HO和ADI方案可以计算出空间四阶精度和时间二阶精度的解。对于 ADI 方案的每个隐式步骤，我们使用高阶紧凑 (HOC) 离散化，以便计算工作仅包含求解三对角系统。为了减少网格点的数量，我们使用组合技术来构建定义在稀疏网格上的解决方案。这种方法可以进一步减少计算量和内存消耗。
In this article we combine the ideas of high-order (HO) and alternating direction implicit (ADI) schemes on sparse grids for diffusion equations with mixed derivatives. With the help of HO and ADI schemes solutions can be computed, which are fourth-order accurate in space and second-order accurate in time. For each implicit step of the ADI scheme we use a high-order-compact (HOC) discretisation such that the computational effort consists of only solving tridiagonal systems. In order to reduce the number of grid points, we use the combination technique to construct a solution defined on the sparse grid. This approach allows to further reduce the computational effort and memory consumption.