The so called (sparse grid) combination technique is an elegant way of combining
the properties of sparse grids, while still being able to use PDE solvers, that support
only standard full grids. Since there are a lot of possible combinations (which don’t
necessarily have to resemble a sparse grid), it is possible to adapt the combination at
runtime to generate more optimal results for each use case, eliminating the need for
manual optimization.
The focus of this project was to implement such an adaptive algorithm in a framework
that only supported the static combination technique. The chosen refining criterion
was based on the difference between the solution of the PDE on two different grids
that are used in the combination. The resulting algorithm was tested with the plasma
physics framework GENE. Due to possibly remaining bugs only basic properties of the
implemented algorithm were examined.
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The so called (sparse grid) combination technique is an elegant way of combining
the properties of sparse grids, while still being able to use PDE solvers, that support
only standard full grids. Since there are a lot of possible combinations (which don’t
necessarily have to resemble a sparse grid), it is possible to adapt the combination at
runtime to generate more optimal results for each use case, eliminating the need for
manual optimization.
The focus of this project was to implement su...
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