A Simple Algebraic Approximate Inverse Preconditioning Scheme for High-Quality-Factor Resonant Cavities

Gemma is a crucial electromagnetic code in the Sandia National Laboratories engineering workflow to simulate the electromagnetic (EM) fields inside and outside complex enclosed cavities that have potential entry points. These simulations are critical for understanding how EM penetration affects internal electronic components, especially when the cavities have high-quality (high-Q) factors. To model such complex problems, Gemma incorporates the method of moments for solving the surface integral equations on the cavity exterior and interior with narrow-slot model that captures the EM coupling between the exterior and the interior. This approach yields an ill-conditioned dense complex-valued linear system. To lighten the heavy burden of direct solvers, Gemma uses a multi-region solver framework accelerated by compression techniques, such as ACA and MLFMA, combined with an iterative solution. The framework not only allows selection of the appropriate solver for each region interaction but also reduces the memory footprint and the computational cost significantly. The framework currently utilizes an additive Schwarz preconditioner, which combines local block-diagonal preconditioners constructed from the different regions self-interaction blocks. Because of extremely ill-conditioned system matrices, robust local preconditioners are desired to maintain the efficiency gained with compression techniques.