Title A New Block-Diagonal Preconditioner for a Class of 3 × 3 Block Saddle Point Problems Type Article Keywords 3 × 3 block saddle point, GMRES, block diagonal, preconditioner, eigenvalue. Abstract We study the performance of a new block preconditioner for a class of 3 × 3 block saddle point problems which arise from finiteelement methods for solving time-dependent Maxwell equations and some other practical problems. We also estimate the lower and upper bounds of eigenvalues of the preconditioned matrix. Finally, we examine our new preconditioner to accelerate the convergence speed of the GMRES method which shows the effectiveness of the preconditioner. Researchers Saeed Karimi (Second researcher) ,