The symmetric Sinc-Galerkin method developed by Lund (Math. Comput. 1986; 47:571-588), when applied to second-order self-adjoint boundary value problems on d dimensional rectangular domains, gives rise to an N × N positive definite coefficient matrix which can be viewed as the sum of d Kronecker products among d - 1 real diagonal matrices and one symmetric Toeplitz-plus-diagonal matrix. Thus, the resulting coefficient matrix has a strong structure so that it can be advantageously used in solving the discrete system. The main contribution of this paper is to present and analyse a multigrid method for these Sinc-Galerkin systems. In particular, we show by numerical examples that the solution of a discrete symmetric Sinc-Galerkin system can be obtained in an optimal way only using O(N log N) arithmetic operations. Numerical examples concerning one- and two-dimensional problems show that the multigrid method is practical and efficient for solving the above symmetric Sinc-Galerkin linear system.

Numerical behaviour of multigrid methods for symmetric Sinc-Galerkin systems

Abstract

The symmetric Sinc-Galerkin method developed by Lund (Math. Comput. 1986; 47:571-588), when applied to second-order self-adjoint boundary value problems on d dimensional rectangular domains, gives rise to an N × N positive definite coefficient matrix which can be viewed as the sum of d Kronecker products among d - 1 real diagonal matrices and one symmetric Toeplitz-plus-diagonal matrix. Thus, the resulting coefficient matrix has a strong structure so that it can be advantageously used in solving the discrete system. The main contribution of this paper is to present and analyse a multigrid method for these Sinc-Galerkin systems. In particular, we show by numerical examples that the solution of a discrete symmetric Sinc-Galerkin system can be obtained in an optimal way only using O(N log N) arithmetic operations. Numerical examples concerning one- and two-dimensional problems show that the multigrid method is practical and efficient for solving the above symmetric Sinc-Galerkin linear system.
Scheda breve Scheda completa Scheda completa (DC)
2005
Multigrid; Preconditioning; Sinc-Galerkin methods; Toeplitz systems
Ng, M. K.; SERRA CAPIZZANO, Stefano; Tablino Possio, C.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11383/1494933`
• ND
• 5
• 6