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The finite-difference (FD) scheme is extensively applied in seismic modelling, imaging and inversion due to its advantages of large-scale parallel computing and programming. However, numerical disp...

The staggered-grid finite-difference method (SGFDM) has been extensively employed in numerical modeling, seismic imaging, and waveform inversion because of its high efficiency, accuracy, and practicality. Numerical modeling accuracy is crucial for imaging and inversion. Truncating the spatial convolution sequence of the pseudospectral method by window functions can derive the finite-difference method. However, truncation error is inevitable; it can create illusions in numerical modeling, leading to misjudgments. To reduce the truncation error and improve numerical modeling accuracy, enhancing the performance of the truncated window function is imperative. In this study, a new optimal window function was investigated based on the least-squares combination of square windows. Then, the new optimized window function was used to truncate the spatial convolution sequence of the pseudospectral method and obtain an optimized SGFDM. Dispersion analysis showed that the optimized SGFDM has wider spectrum coverage than the conventional SGFDM at the same order. In addition, at low orders, the error range of the new optimized SGFDM could be strictly controlled within 1‱, whereas, at high orders, while ensuring accuracy, the spectrum coverage significantly improved. Finally, numerical modeling for elastic waves demonstrated that the optimized SGFDM could superiorly suppress numerical dispersion and improve calculation efficiency.

This chapter provides implementation of various optimization algorithms to various power system problems that utilize power flow calculations. Determination of the schedule (ON/OFF status and amount of power generated) of generating units within a power system results in great saving for electric utilities. The unit commitment problem can be formulated in order to minimize the total operating cost, satisfying the system, the unit, and several operational constraints. The power transfer limit of overhead transmission lines (OTLs) is an important constraint for power systems’ planning and operation. This constraint plays an essential role in the secure and economic management of power systems. The chapter presents economic dispatch problem by considering GAs and particle swarm optimization (PSO) in complex power system analysis. It uses a hybrid PSO to solve load flow problem while uses artificial bee colony optimization for solving the optimal power flow problem.

The staggered-grid finite-difference (SGFD) method is one of the most popular means used in seismic numerical modelling because of its computational efficiency and it is easy to implement. However, it will lead to serious numerical errors while using coarse grids or wavelet with high-frequency. In this work, we proposed an optimal spatial SGFD method based on a new improved particle swarm optimization (PSO) algorithm. Then the dispersion of numerical solution of the first-order spatial derivatives is analyzed. Meanwhile, numerical modelling of elastic wave equations and elastic wave equations including rotational deformation are performed with the optimal spatial SGFD method based on the improved PSO algorithm. Numerical dispersion analysis and numerical modeling results indicate that the optimal spatial SGFD method based on the improved PSO algorithm has high modeling accuracy and can efficiently suppress the numerical dispersion.