| The objective of this dissertation is to present an efficient parallel implementation of the iterative compact high-order approximation numerical solver for the forward problem of the subsurface scattering problems derived from the 3D Helmholtz equation. The high-order parallel iterative algorithm is built upon a combination of the generalized minimum residual method (GMRES) method with a direct Fast Fourier transform (FFT) type preconditioner from the authors’ previous work in [37]. High-order compact finite differences schemes are used to compute high-resolution numerical solutions. The performance of the proposed algorithm will be tested by computationally simulating data with realistic ranges of parameters in soil and mine-like targets. Additionally, the application of the proposed numerical solver can be extended to computer numerical solutions for other partial differential equations (PDE) such as 3D convection-diffusion equations. The proposed algorithm represents a highly parallelizable iterative algorithm suitable for excellent performance under various parallel environments. |