  An exact arithmetic, memory efficient direct solution method for finite
element method (FEM) computations is outlined. Unlike conventional black-box or
low-rank direct solvers that are opaque to the underlying physical problem, the
proposed method leverages physical insights at every stage of the development
through a new symmetric domain decomposition method (DDM) with one set of
Lagrange multipliers. Comparisons with state-of-the-art exact direct solvers on
electrically large problems suggest up to 10 times less memory and better
run-time complexity while maintaining the same accuracy.
