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{\large Lior Horesh \\
{\bf Generic approach for construction of high-order discrete differential operators for OcTree structures}}

IBM TJ Watson Research Center \\ 1101 Kitchawan Rd \\ Yorktown Heights \\ NY \\ 10598
\\
{\tt lhoresh@us.ibm.com}\\
Eldad Haber\\
Andrew R Conn\end{center}

In this study, a generic framework for high-order OcTree discretization
is proposed. OcTree discretization offers unique advantages in the
solution of large-scale problems; however, its unstructured grid nature
requires special means for the construction of discrete operators. As
opposed to the conventional approach in which operators are prescribed
and analysis is practiced for error assessment, here the discretization
operators are directly derived from the analysis. This is conducted
through a two stage process in which the support for each component of
the discrete operator is first queried and then, interpolation conditions
yield local systems which are solved to provide the desired irregular
difference templates. We show that this approach allows for the accurate
and effective solution of large-scale systems evolving from Maxwell's
equations. We further explore the usage of these operators as a
complementary measure for local refinement.


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