Compressible integral equation formulations towards general fast direct solvers

The challenge of deriving a surface integral equation formulation that will be inherently compressible, for the purpose of designing general fast direct solvers, is addressed. Preliminary attempts to develop generalized equivalence and generalized source formulation-based solvers are presented. The limitations arising from these newly introduced generalized formulations on the direct solvers' accuracy for geometries of general shape are discussed towards further extensions.