高性能计算技术及其在电磁散射中的应用研究
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摘要
高性能计算(High Performance Computing, HPC)是计算机科学的一个重要分支,它是研究并行算法和并行计算机体系结构的学科。随着信息化社会的飞速发展,传统单机运算速度和容量遇到硬件瓶颈,高性能计算受到广泛重视,而高性能计算水平已成为衡量一个国家科研能力的标志之一。在一些学科,如计算力学、电磁散射和生物科学领域,高性能计算平台已成为科学研究的必备工具。
电磁散射在军事和工程领域均有广泛应用,本文研究钻井探测中的微波散射现象。探测方法研究涉及计算机并行处理、计算数学和计算电磁学等多个学科,是一门综合的多领域交叉科学。钻井微波探测工具在近几十年获得持续高速发展,其在石油、天然气等地下资源的勘探发掘中起关键作用。钻井挖掘方法从垂直勘探、倾斜勘探到可扩展侧向伸展勘探,使得每次挖掘可获得更广袤地域的地下信息。探测工具中的天线经历了从极子天线、环型天线到倾斜环型天线,使得工具可探测更多地质层中的介质信息。
本文对钻井微波探测中的时域和频域并行仿真方法进行研究。提出在时域方法中采用无条件稳定策略,同时利用模型(部分)旋转对称的特性,对问题进行分解简化,以加快算法的处理速度。在频域方法中,伪解析法作为一种半解析半数值的方法,具有速度快、精度高的优点,但之前研究对象均为各向同性介质。本文研究更复杂介质的情况,并将伪解析法推广到轴各向异性地质介质,分析和实验均显示出这种方法的优越性。传播矩阵法作为伪解析法的一种推广形式,其适用性更强,文中用传播矩阵方法分析了全各向异性以及轴向非均匀地质介质。本文围绕一种目前主流的钻井微波探测工具—随转探测微波工具(Logging While Drilling, LWD),对几种主要的仿真方法进行了深入研究,主要工作可列举如下:
一、对在柱坐标系中几种主要的时域有限差分方法(Finite-Difference Time-Domain, FDTD)进行了研究,主要侧重无条件稳定的时域方法。交替方向隐式(Alternating Direction Implicit, ADI)FDTD方法可模拟细网格模型,但却有分步误差。我们提出一种矫正策略,引入一个近似项对误差进行修正,实验分析表明,此策略可将分步误差从三阶精度提高到四阶精度。文中对另一种无条件稳定方法,局部一维(Locally One-Dimension, LOD)FDTD方法的任意阶精度格式进行了分析,给出一致性数值色散关系,并对高阶收敛性进行了分析证明。
二、结合钻井工具的工作环境,讨论了旋转对称结构(Body-Of-Rotation)中FDTD方法的数值特性。并将Crank-Nicolson(CN)FDTD方法推广到旋转对称结构,首次给出CN-BOR-FDTD方法的计算公式,并将其用于钻井探测工具模型LWD中。CN-FDTD方法的计算时间较ADI-FDTD方法和LOD-FDTD方法长,但不含分步误差,而采用BOR策略可有效节约计算时间。实验证明CN-BOR-FDTD方法是一种快速准确的时域方法。
三、伪解析法作为一种半解析半数值方法,具有速度快精度高的特点,但其适用的环境受到很大限制。已有研究均假设钻井环境中地质层是各向同性介质,但由于重力等因素,岩层中介质在水平和垂直方向表现出不同的电磁特性。文中讨论了Maxwell方程在轴各向异性中特征函数展开形式,首次将伪解析法推广到轴各向异性地质层的情况。提出归一化策略,可计算任何(大)尺寸问题,并采用迭代格式避免在求解过程中使用病态矩阵逆运算。这种方法可用半径无限大的圆来近似模拟岩层直线边界的情况,是一种快速、实用的方法。
四、提出用传播矩阵法计算更复杂地质层介质模型。传播矩阵法作为伪解析法的一种推广,可用于计算更加复杂的介质模型。我们全面系统的推导了在轴各向异性介质、全各向异性介质和轴向非均匀介质中传播矩阵法的计算公式。与伪解析法进行对比验证的结果表明,传播矩阵方法同样具有很高计算精度。另外用传播矩阵法分析了凿洞中液体在周围地质层中非均匀扩散时,钻井微波探测工具的响应情况。
本文所有算法均通过编程实现,大部分算法经并行化处理,其中一部分在集群多机并行环境下通过验证,其余部分在美国俄亥俄州超级计算中心高性能计算平台Glenn上通过验证。另外对某些算法性能给出了理论分析。
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.
电磁散射在军事和工程领域均有广泛应用,本文研究钻井探测中的微波散射现象。探测方法研究涉及计算机并行处理、计算数学和计算电磁学等多个学科,是一门综合的多领域交叉科学。钻井微波探测工具在近几十年获得持续高速发展,其在石油、天然气等地下资源的勘探发掘中起关键作用。钻井挖掘方法从垂直勘探、倾斜勘探到可扩展侧向伸展勘探,使得每次挖掘可获得更广袤地域的地下信息。探测工具中的天线经历了从极子天线、环型天线到倾斜环型天线,使得工具可探测更多地质层中的介质信息。
本文对钻井微波探测中的时域和频域并行仿真方法进行研究。提出在时域方法中采用无条件稳定策略,同时利用模型(部分)旋转对称的特性,对问题进行分解简化,以加快算法的处理速度。在频域方法中,伪解析法作为一种半解析半数值的方法,具有速度快、精度高的优点,但之前研究对象均为各向同性介质。本文研究更复杂介质的情况,并将伪解析法推广到轴各向异性地质介质,分析和实验均显示出这种方法的优越性。传播矩阵法作为伪解析法的一种推广形式,其适用性更强,文中用传播矩阵方法分析了全各向异性以及轴向非均匀地质介质。本文围绕一种目前主流的钻井微波探测工具—随转探测微波工具(Logging While Drilling, LWD),对几种主要的仿真方法进行了深入研究,主要工作可列举如下:
一、对在柱坐标系中几种主要的时域有限差分方法(Finite-Difference Time-Domain, FDTD)进行了研究,主要侧重无条件稳定的时域方法。交替方向隐式(Alternating Direction Implicit, ADI)FDTD方法可模拟细网格模型,但却有分步误差。我们提出一种矫正策略,引入一个近似项对误差进行修正,实验分析表明,此策略可将分步误差从三阶精度提高到四阶精度。文中对另一种无条件稳定方法,局部一维(Locally One-Dimension, LOD)FDTD方法的任意阶精度格式进行了分析,给出一致性数值色散关系,并对高阶收敛性进行了分析证明。
二、结合钻井工具的工作环境,讨论了旋转对称结构(Body-Of-Rotation)中FDTD方法的数值特性。并将Crank-Nicolson(CN)FDTD方法推广到旋转对称结构,首次给出CN-BOR-FDTD方法的计算公式,并将其用于钻井探测工具模型LWD中。CN-FDTD方法的计算时间较ADI-FDTD方法和LOD-FDTD方法长,但不含分步误差,而采用BOR策略可有效节约计算时间。实验证明CN-BOR-FDTD方法是一种快速准确的时域方法。
三、伪解析法作为一种半解析半数值方法,具有速度快精度高的特点,但其适用的环境受到很大限制。已有研究均假设钻井环境中地质层是各向同性介质,但由于重力等因素,岩层中介质在水平和垂直方向表现出不同的电磁特性。文中讨论了Maxwell方程在轴各向异性中特征函数展开形式,首次将伪解析法推广到轴各向异性地质层的情况。提出归一化策略,可计算任何(大)尺寸问题,并采用迭代格式避免在求解过程中使用病态矩阵逆运算。这种方法可用半径无限大的圆来近似模拟岩层直线边界的情况,是一种快速、实用的方法。
四、提出用传播矩阵法计算更复杂地质层介质模型。传播矩阵法作为伪解析法的一种推广,可用于计算更加复杂的介质模型。我们全面系统的推导了在轴各向异性介质、全各向异性介质和轴向非均匀介质中传播矩阵法的计算公式。与伪解析法进行对比验证的结果表明,传播矩阵方法同样具有很高计算精度。另外用传播矩阵法分析了凿洞中液体在周围地质层中非均匀扩散时,钻井微波探测工具的响应情况。
本文所有算法均通过编程实现,大部分算法经并行化处理,其中一部分在集群多机并行环境下通过验证,其余部分在美国俄亥俄州超级计算中心高性能计算平台Glenn上通过验证。另外对某些算法性能给出了理论分析。
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.
引文
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