January 2007
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An Improved H-curl Algebraic Multigrid Solver for Z-pinch Simulations

Alegra-HEDPSandia’s ML solver team has resolved an extremely challenging technical issue associated with the solution of singular and ill-conditioned H(curl) matrices for ALEGRA-HEDP Z-pinch simulations.
A parallel H(curl) algebraic multigrid solver was adapted to address conductivity variations ranging over eight orders of magnitude as well as to allow for regions of zero conductivity (or void regions). These extreme conditions require special care in how operators are coarsened and how errors are smoothed within the solver. Simulations involving large conductivity variations and significant mesh stretching are needed for highly accurate simulations that avoid spurious magnetic Rayleigh-Taylor instabilities in the overall solution of a liner implosion problem.

As a result of efforts in both linear solvers and in the proper numerical representation of the underlying physics, a simulation recently and for the first time ran through the peak of the main power pulse without exhibiting magnetic Rayleigh Taylor instability induced by background noise. The intended symmetric magnetic field solution was produced. This achievement is an important step toward modeling and simulation of Z-pinch phenomena.

Linear implodesSubsequent simulations will allow analysts to determine the effects of slots and gaps on system behavior, which will be relevant in determining how to redesign the load to eliminate undesirable features in experiments on the Z-machine. The solver enhancements have been incorporated in the Trilinos Library and represent a substantial advance in the solvability of H(curl) systems arising during Z-pinch simulations. A completely new H(curl) algebraic multigrid solver is also under development. This new solver is based on an exact discrete algebraic reformulation of the H(curl) problem and takes advantage of a discrete Hodge decomposition. Numerical experiments indicate that this future H(curl) solver will be even less sensitive to the dramatic material variations common in Z-pinch experiments.