Sparse direct solution of the electric field integral equation using nonoverlapped localizing logos modes

Abstract

These results are also in agreement with the experimental ones, apart from experimental errors. It is noteworthy that the numerical calculation of the noise figure is very dependent on the initial ASE power of the WDM channels.The noise figure is approximately the same for coherent and incoherent pumping in the counter propagation configuration. CONCLUSIONSWe report an incoherent Raman amplification scheme with a low cost pump source.In agreement with previous works [1-6], our results indicate that incoherent pumping decreases the spectral ripple of the Raman gain, which corresponds to a decrease of the gain slope.Furthermore, a good agreement between experimental and simulation results was achieved with the present numerical model.

Error Analysis for Matrix Factorizations Using Non-Overlapped Localizing Basis Functions

“…In the worst case, when condr j p N L , (18) can result in an increased error in factorization of NL times [compare (18) with (14)]. In all test cases studied in this work, (18) provides good error control. However, for precise error control, (17) should be used to check the error condition once a given value of N L is determined via (18).…”

“…In all test cases studied in this work, (18) provides good error control. However, for precise error control, (17) should be used to check the error condition once a given value of N L is determined via (18).…”

“…The benefit of using (18) is that the computation of cond(rj) is not required, the cost of which increases as the problem's size grows. In the worst case, when condr j p N L , (18) can result in an increased error in factorization of NL times [compare (18) with (14)]. In all test cases studied in this work, (18) provides good error control.…”

“…The error control formulae for determining localizing source modes are given by (17) or (18). The tolerances used in (17) or (18) for multilevel factorization should be scaled according to (21).…”

“…It has recently been observed that the LOGOS framework [12]- [18], [22]- [25] provides a systematic strategy for developing sparse factorizations of Z and, consequently, fast direct solutions of (1). The fast direct solution algorithms outlined in [12]- [15], [17], [18], [26]- [31] utilize non-overlapped, localizing LOGOS (NL-LOGOS) modes to factor the system matrix. The computational complexity of the resulting factorizations scale as O(N 1:502 ) for 3D surface integral equation problems when the object is smaller than a few wavelengths in general.…”