An Accuracy Improvement in Solving Scalar Wave Equation by Finite Difference Method in Frequency Domain Using 49 Points Weighted Average Method

주파수영역에서 49점 가중평균을 이용한 scalar 파동방정식의 유한차분식 정확도 향상을 위한 연구

Much computing time and large computer memory are needed to solve the wave equation in a large complex subsurface layer using finite difference method. The time and memory can be reduced by decreasing the number of grid per minimun wave length. However, decrease of grid may cause numerical dispersion and poor accuracy. In this study, we present 49 points weighted average method which save the computing time and memory and improve the accuracy. This method applies a new weighted average to the coordinate determined by transforming the coordinate of conventional 5 points finite difference stars to $0^{\circ}$ and $45^{\circ}$, 25 points finite differenc stars to $0^{\circ}$, $26.56^{\circ}$, $45^{\circ}$, $63.44^{\circ}$ and 49 finite difference stars to $0^{\circ}$, $18.43^{\circ}$, $33.69^{\circ}$, $45^{\circ}$, $56.30^{\circ}$, $71.56^{\circ}$. By this method, the grid points per minimum wave length can be reduced to 2.5, the computing time to $(2.5/13)^3$, and the required core memory to $(2.5/13)^4$ computing with the conventional method.