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This paper introduces a new spontaneous potential log model for the case in which formation resistivity is not piecewise constant. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on the interfaces. It has been shown that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic problems. Numerical results show validity and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We present effective methods for the numerical simulation of high-power-pumped continuous-wave (CW) and pulsed erbium-ytterbium-codoped fiber amplifiers (EYDFAs). For CW EYDFAs, a novel initial guess method and a robust algorithm are proposed to ensure the convergence of the boundary-value problems involved in the solution of the numerical model. For pulsed EYDFAs, an efficient finite-difference method based on the Lax-Wendroff scheme is developed. With these methods, high-power CW or pulsed EYDFAs can be simulated. As an example, a high-power pulse-pumped low repetition rate EYDFA is analyzed. Besides demonstrating the proposed methods, the simulation results show that the optimal pulse width of the pump can be determined by the power of the backward Yb-ASE, and the time delay between the signal and pump pulses play an important role in optimizing the performance of a high power pulse-pumped EYDFA. [ABSTRACT FROM AUTHOR]