High Performance Computing Technology And Its Application In Electromagnetic Scattering

High Performance Computing (HPC) is one of the important branches of the Computer Science, in which the researches involve the parallel algorithms and parallel computer framework. As the development of information industry, the capabilities of computation of single computer have encountered the physical hardware bottleneck. The HPC technology has received more and more attention. It becomes a scale of scientific research for each country. In some fields, such as Computational Mechanics, Electromagnetic Scattering and Bioinformation et.al., parallel computing plat is a necessary toolkit.Electromagnetic Scattering has various applications in both of civil and military engineering. In this paper, we study the phenomena of the electromagnetic scattering of electrical well-logging. Microwave detecting techniques involve the knowledge of Parallel Computing, Computational Mathematics and Computational Electromagnetics. It is a cross field of many subjects. Tools for electrical well-logging have been developed rapidly in these decades. Its applications play key roles in the exploration of subsurface resource, such as oil and gas etc. The approach in drilling well has been improved from vertical well, directional well to extended-reach well, in order to extending their physical coverage. The antennas used in Electrical Well-Logging tools have changed from dipole antennas, coil antennas and tilted coil antennas, in order to getting more sensitivity for the medium of subsurface beds.In this paper, both of the methods in time-domain and frequency-domain are studied. We proposed the hybrid implementation of unconditionally stable time-domain finite-difference scheme and the Body-Of-Rotation (BOR) scheme. The BOR scheme takes the advantage of (partially) axial symmetry in the environment of Well-Logging to accelerate the code. Among the frequency-domain methods, the pseudo-analytical method, which is a semi-analytical and semi-numerical method, has the virtue of computational effectiveness and high accuracy. However, the previous researches are based on the assumption of isotropic medium. In this paper, we studied the complex medium. The pseudo-analytical method has been extended for axially anisotropic medium. The experiences have validated the effectiveness of the new pseudo-analytical method. We derived the formulas of the propagator matrix method for the model of Electrical Well Logging tools. This method is an extension of the pseudo-analytical method, with much more applicable fields. By using the propagator matrix method, the medium of full anisotropy and radial inhomogeneity are studied. Involving the classical Electrical Well Logging tool, Logging-While-Drilling (LWD) tool, several main simulation algorithms have been discussed. The main works can be summarized as following:(I) Several main cylindrical Finite-Difference Time-Domain (FDTD) methods are studied, emphasizing the time-domain methods with unconditionally stability. The Alternating-Direction-Implicit (ADI) FDTD method is suitable for fine grid model. However, it involves splitting error. We proposed a correction scheme, in which an approximation term is introduced to reduce the splitting error. Numerical analysis shows that the error has been reduced from third-order to four-order. Meanwhile, we analyze the performance of higher-order Locally One-Dimension (LOD) FDTD methods. We have presented the uniform formulas of their numerical dispersion relationship, and proved the convergence as the order increases.(II) Based on the environment where LWD is applied, we discuss the numerical properties of the BOR-FDTD methods. The BOR scheme is utilized into Crank-Nicolson (CN) FDTD method, and the updating equations for the CN-BOR-FDTD method are given to simulate the LWD tools. The CN-FDTD method takes more computational time than those of the ADI-FDTD method and the LOD-FDTD method, but with no splitting error. The BOR scheme can reduce the computational time sharply. Numerical experiments show that the CN-BOR-FDTD method is an effective and accurate time-domain method.(III) The pseudo-analytical method, combination of analytical method and numerical method, can achieve high computational accuracy and require low computer time. However, the range of the application of the pseudo-analytical method is very limited. All of the previous researches on the pseudo-analytical method in LWD model are based on the assumption of isotropic medium. Due to the effect of gravity etc., Earth formations exhibit anisotropic conductivities, in which the vertical components may differ from the horizontal ones. In this work, we extend the pseudo-analytical method to anisotropic Earth formations. The formalism is based on an expansion of the field components in terms of the appropriate cylindrical eigenfunctions in uniaxial anisotropic media. A normalized scheme is proposed to simulate arbitrary-size geometry. An iterative solver is applied to overcome the inversion of ill-conditioned matrix as well. The proposed can also simulate the flat bed boundary by a circle of sufficiently large radius. Numerical experiments validate its efficiency.(IV) The propagator matrix method is proposed to handle complex Earth formations. This method is an extension of the pseudo-analytical method, by which we can simulate complex medium. The formulism of the propagator matrix method for uniaxial anisotropic medium and full anisotropic medium are derived. Compared with results of the pseudo-analytical method, the propagator matrix method has similar accuracy. The response of the well-logging tools for the inhomogeneous penetration of the borehole liquid into Earth formation is investigated by using the propagator matrix method.All of the algorithms mentioned in this paper are implemented by computer programming. Most of them have been parallelized. Some parallelized codes run on cluster environment, and the others run on the plat of Ohio State Supercomputing Center, named Glenn. We also give theoretical analysis for the performance of some algorithms.