Symmetric sparse approximate inverse preconditioners for combined field integral equation

A symmetric sparse approximate inverse (S-SAI) preconditioners for the combined field integral equation (CFIE) is presented in this paper. The asymmetric matrix arising from the CFIE is transformed into a symmetric one, which is employed for efficiently constructing preconditioner by the Cholesky factorization. Numerical experiments show that this S-SAI preconditioner has similar convergent behavior to the previous asymmetric sparse approximate inverse (A-SAI) one, but the construction time of it can be cut down by a factor of at least 32 than that of A-SAI.