Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4644905 | Applied Numerical Mathematics | 2016 | 17 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Computational Mathematics
Authors
Christian Hendricks, Matthias Ehrhardt, Michael Günther,