### Theory Weekly Highlights for January 2000

##### January 28, 2000

A proof of principle software engineering experiment was completed where EFIT was wrapped in the MPI environment allowing simultaneous EFIT code runs to be executed on 3 different Linux CPUs. The benefit of this environment is that DIII-D shot data is only collected once and the data is then passed to each CPU as it is needed. When the new 12 processor Linux system arrives, EFIT with MPI will move seamlessly to this system giving the DIII-D research team between shot EFITs on a much faster time scale.

##### January 21, 2000

The source of the numerical problem in the 2D version of the TWIST-R resistive MHD stability code has been found by developing a 1D version of the code and comparing the results between the 1D and 2D codes for a specially constructed model cylindrical equilibrium. The TWIST-R code uses a newly developed numerical technique for solving a general set of coupled differential equations with singular solutions, by analytically transforming to a set of equations with regular solutions and performing the back transformation once the numerical solution is found. Numerical tests with 1D problems have previously shown extremely good convergence, numerical stability, and accuracy, but implementation in 2D, solving for both the normal and tangential displacement, revealed a numerical problem manifested as a loss of convergence. The problem appears to be analogous to the spectral pollution, which appears in 2D ideal MHD Finite Element stability codes when the tangential displacement is numerically solved for. However, the same cures are not directly applicable in TWIST-R, since TWIST-R is not variational and uses a finite difference scheme. Also, we have shown that for the 1D problem, small numerical errors in the tangential displacement are amplified in this case, in contrast to the ideal case where the singular solution is not present. Nevertheless, several possibilities, in which these errors are eliminated or suppressed have been shown to work in the 1D case, and 2D implementations are under consideration.

**Disclaimer**

These highlights are reports of research work in progress and are accordingly subject to change or modification

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