AbstractA new parallel normalized optimized approximate inverse algorithm, based on the concept of antidiagonal wave pattern, for computing classes of explicitly approximate inverses, is introduced for symmetric multiprocessor systems. The parallel normalized explicit approximate inverses are used in conjunction with parallel normalized explicit preconditioned conjugate gradient schemes for the efficient solution of finite element sparse linear systems. The parallel design and implementation issues of the new algorithm are discussed and the parallel performance is presented using OpenMP. Copyright © 2008 John Wiley & Sons, Ltd.