Accurate solution of time-dependent, high-dimensional PDEs requires massive-scale parallel computing and efficient numerical techniques. Spatial decomposition is particularly challenging in higher dimensions, since the memory requirements for uniform grids with fine enough resolution quickly grow prohibitively large and out of reach even for massively parallel computers. The HAParaNDA-project is an attempt at pushing the limit of tractable problems by using adaptive numerical techniques in time and space together with efficient exponential integrators for propagation in time.

1. Impact of code refactoring using object-oriented methodology on a scientific computing application. Malin Källén, Sverker Holmgren, and Ebba þóra Hvannberg. In Proc. 14th International Working Conference on Source Code Analysis and Manipulation, pp 125-134, IEEE Computer Society, Los Alamitos, CA, 2014. (DOI).
2. Communication-efficient algorithms for numerical quantum dynamics. Magnus Gustafsson, Katharina Kormann, and Sverker Holmgren. In Applied Parallel and Scientific Computing: Part II, volume 7134 of Lecture Notes in Computer Science, pp 368-378, Springer-Verlag, Berlin, 2012. (DOI).
3. Numerical evaluation of the Communication-Avoiding Lanczos algorithm. Magnus Gustafsson, James Demmel, and Sverker Holmgren. Technical report / Department of Information Technology, Uppsala University nr 2012-001, 2012. (fulltext).
4. Stable difference methods for block-structured adaptive grids. Magnus Gustafsson, Anna Nissen, and Katharina Kormann. Technical report / Department of Information Technology, Uppsala University nr 2011-022, 2011. (External link, fulltext).
5. An implementation framework for solving high-dimensional PDEs on massively parallel computers. Magnus Gustafsson and Sverker Holmgren. In Numerical Mathematics and Advanced Applications: 2009, pp 417-424, Springer-Verlag, Berlin, 2010. (DOI).

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