Improved c methods for transient wave scattering

다국어 초록 (Multilingual Abstract)

As a consequence of the rapid development of computers, there is a strong interest in the solution of larger and larger scattering problems. In particular, radar cross section (RCS) problems which involve typically scattering From complex targets many wavelengths long are of considerable interest. Though there exist many numerical methods which are suitable for RCS problems, the boundary integral equation (BIE) method is one of the more efficient tools for their analysis, with costs scaling with the fifth power of the incident frequency. The algorithm modifications described here offer the prospect of large reductions in cost, and a possible reduction in cost scaling to the fourth power of the frequency. This has been achieved by the combination of a re-ordering of the normal BIE algorithm to a "project forward" form, and implementation of a modest further physical approximation which this re-ordering makes possible. This approach is demonstrated for a variety of geometries, including relatively difficult ones such as the NASA almond and cone-sphere and gap benchmarks.
The project forward algorithm has some advantages over the normal retrospective algorithm both in parallelisation and in hybridisation with time domain physical optics (POTD). The parallelisation and hybridisation of the project forward algorithm are developed in this thesis and their results are demonstrated. The results show that the project forward algorithm is very effective in such analysis.

목차 (Table of Contents)

• List of Figures and Tables = 9
• Chapter 1. Introduction = 14
• 1.1 Overview of the Thesis = 14
• 1.2 Large EM Wave Scattering Problems = 17
• 1.3 Methods for EM Wave Scattering Problems = 17
• 1.3.1 Optical Methods = 19
• 1.3.2 Integal Equation Methods = 20
• 1.3.3 Differential Equation Methods = 21
• 1.3.4 Hybrid Methods = 23
• Chapter 2 Time Domain Boundary Integral Equation Method for EM Wave Scattering Problems = 25
• 2.1 Derivation of the Magnetic Field Integral Equation = 25
• 2.2 Computational Issues for the Governing Equation = 46
• 2.2.1 Geometry Representafiions = 46
• 2.2.2 Field Representation in Space and Time = 47
• 2.2.3 Integration = 48
• 2.2.4 Implicitness, Explicitness and Stability = 50
• 2.3 Numerical Discretisation of MFIE = 52
• 2.3.1 Geometry Representation = 52
• 2.3.2 Field Representation in Space and Time = 54
• 2.3.3 Integration = 56
• 2.3.4 Implicitness, Explicitness and Stability = 61
• 2.3.5 Matrix Solution = 62
• 2.4 Pulsed Excitation = 63
• 2.5 Cost Scaling of BIEM for RCS problems = 64
• 2.6 Computational Implementation of BIEM = 67
• 2.6.1 Pre-Processing = 67
• 2.6.2 Surface Current Calculation = 68
• 2.6.3 Far Field Solution = 68
• 2.7 Some Examples of Electromagnetic Scattering Problems = 69
• 2.7.1 Sphere = 69
• 2,7.2 Choosing the Pulse Width = 69
• 2.7.3 NASA Almond = 71
• 2.8 Discussion = 71
• Chapter 3 Physical Basis for the Computational Cost Reduction = 82
• 3.1 Introduction = 82
• 3.2 Physical Basis of Cost Saving = 83
• 3.3 Thresholding Results = 85
• 3.3.1 10:1 Dipole = 85
• 3.3.2 Bent Dipole = 86
• 3.3.3 NASA Almond = 87
• 3.4 Discussion = 88
• Chapter 4 Modification of the BIE Algorithm to Implement Cost Reduction = 93
• 4.1 Introduction = 93
• 4.2 Description of the Modified Algorithm = 95
• 4.3 Computational Implementation of the Method = 101
• 4.3.1 'not on the fly' Calculation = 103
• 4.3.2 'on the fly' Calculation = 104
• 4.4 Discussion = 105
• Chapter 5 Parallelisation of the Project Forward Algorithm = 107
• 5.1 Parallel Computation = 107
• 5.1.1 Architecture of Parallel Computers = 108
• 5.1.2 Parallel Implementation = 108
• 5.1.3 Parallel Performance Metrics = 109
• 5.2 Parallelisation of the Time Domain Integral Equation Method = 110
• 5.3 Parallelisation of the Project Forward Algorithm = 112
• 5.4 Parallelisation of the Matrix Solver = 114
• 5.5 Computational Implementation of the Method = 115
• 5.6 Discussion = 116
• Chapter 6 Results of the Modified Algorithm = 119
• 6.1 Accuracy, Cost and Thresholds = 119
• 6.1.1 Spheres 1.3 and 4 Wavelengths in Diameter = 119
• 6.1.2 NASA Almond = 121
• 6.2 Cost Scaling = 122
• 6.3 Computational Work, and Active and Quiescent Regions = 125
• 6.4 Perfectly Conducting Cone-Sphere with Gap = 127
• 6.5 Performance of the Parallel Algorithm = 128
• Chapter 7 Hybridisation of the Project Forward Algorithm = 141
• 7.1 Introduction = 142
• 7.2 Hybridisation of the Time Domain Integral Equation Method = 143
• 7.3 Hybridisation of the Project Forward Algorithm = 145
• 7.4 Results = 145
• 7.4.1 Correctness of Hybridisation = 146
• 7.4.2 Ball and Plate = 146
• 7.4.3 Missile on Wing = 147
• 7.5 Discussion = 148
• Chapter 8 Conclusion = 156
• Appendix = 159
• A. Termination Criteria in Iterative Solutions of Large Scattering Problems Using Integral Equation Methods = 160
• References = 175