Solution of Simultaneous Partial Differential Equations Using Dynamic ADI: Solution of the Streamlined Darwin Field Equations

We apply a particular version of ADI called Dynamic ADI (DADI) to the strongly coupled 2nd-order partial differential equations that arise from the streamlined Darwin field (SDF) equations. The DADI method is applied in a form that we show is guaranteed to converge to the desired solution of the finite difference equation. We give overviews of our test case, the SDF problem, and the DADI method, with some justification for our choice of operator splitting. Finally, we apply DADI to the strongly coupled SDF equations and present the results from our test case. Our implementation requires a factor of 7 less storage and has proven to be a factor of 4 (in the worst case) to several orders of magnitude faster than competing methods.