PRECONDITIONING ON ELEMENT INTERFACES FOR THE p-VERSION FINITE ELEMENT METHOD AND SPECTRAL ELEMENT METHOD

Abstract. In the preconditioned iterative method based on nonoverlapping domain decompo-sitions, the preconditioner is usually of block diagonal type. To calculate its action on a residual vector, it is required to solve a linear system of algebraic equations with the coecient matrix being the Schur complement block corresponding to the interface. To reduce the computational cost, the Schur complement blocks in the preconditioners can be replaced with other simpler matrices, which are called the interface preconditioners. In this paper, we discuss various interface preconditioners for the p-version nite element method and spectral element method in R2 and R3. Emphases are placed on (1) the lower and upper bounds of the condition numbers for the preconditioned Schur com-plement blocks using the interface preconditioners, which characterize the enlargement of the overall condition numbers, and (2) the algorithms to eciently implement the interface preconditioners. Numerical results are presented for the condition numbers using various interface preconditioners. Key words. preconditioning, element interface, the p-version, spectral element method, condi-tion number AMS subject classications. 65F10, 65N30, 65N55 PII. S1064827596306951 1. Introduction. Fo