been carried out on a Pentium III 662-MHz Xeon PC with a 512-Mb RAM, and a residual error of 0.001 has been chosen as the convergence criterion for the iterative solvers. The CPU time shown for the iterative solvers includes the time taken for equilibration and for generation of the preconditioner matrix, as well as the time needed by the iterative solver itself. All the computations have been carried out in double-precision arithmetic. It is seen that both the iterative solvers are considerably faster than the direct solver even for poorly conditioned matrices with a small number of unknowns. The GMRES solver exhibited better performance and took less than 10 iterations irrespective of the number of unknowns. For a comparable number of iterations (Cases b and d), the CGNR solver took nearly twice the CPU time compared to the GMRES solver due to the additional operations involving the adjoint operator.
CONCLUSIONA simple and efficient approach has been presented for preconditioning a large dense system of linear equations arising in the integral-equation formulation of electromagnetic problems. A twostep process is introduced, which the condition number of the matrix is first improved by equilibration, and is further enhanced by preconditioning in the second step. It has been shown that the proposed technique improves the computational efficiency of the iterative solvers, for example, CGNR and GMRES, even for poorly conditioned MoM matrices with a relatively small number of unknowns. It is expected that the method would find useful applications for the efficient solution of a wide variety of electromagnetic problems efficiently.
DISCRIMINATION BETWEEN STRAIN AND TEMPERATURE WITH A SINGLE FIBER BRAGG GRATING
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