Sparse factorization techniques

If Equation 15-34 is to be written for each (i,j,k) node and solved at the new time step (n+1), we obtain a complicated system of algebraic equations that is costly to invert computationally. When it cannot be locally linearized, the full but sparse matrix is solved using even more expensive Newton-Raphson iterations. Thus, we employ approximate factorization techniques to resolve the system into three simpler, but sequential banded ones. In this approach. 

Human error probabilities can also be estimated using methodologies and techniques originally developed in the nuclear industry. A number of different models are available (Swain, Comparative Evaluation of Methods for Human Reliability Analysis, GRS Project RS 688, 1988). This estimation process should be done with great care, as many factors can affect the reliability of the estimates. Methodologies using expert opinion to obtain failure rate and probability estimates have also been used where there is sparse or inappropriate data. 

This relationship of the impedance as a complex function, shown in Equation 8.8, is often the reason that MXC researchers sometimes look at EIS as a complicated, mysterious technique. We believe that this may be a contributing factor to the sparse and incomplete application of EIS in MXC studies. The principles of EIS have foundations in basic mathematics of complex numbers. As we apply sinusoidal amplitude on voltage, both the voltage and the current with time have to be represented as a sine function, and it is through Euler s formula that these and the resulting impedance can be represented as complex functions. 

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