Dennis M. Sullivan - Electromagnetic Simulation Using the FDTD Method with Python

9 5 ADVANCED PYTHON FEATURES 5.1 CLASSES PROBLEM SET 5.1 5.2 PROGRAM STRUCTURE PROBLEM SET 5.2.1 PROBLEM SET 5.2.2 5.3 INTERACTIVE WIDGETS PROBLEM SET 5.3

10 6 DEEP REGIONAL HYPERTHERMIA TREATMENT PLANNING 6.1 INTRODUCTION 6.2 FDTD SIMULATION OF THE SIGMA 60 6.3 SIMULATION PROCEDURE 6.4 DISCUSSION REFERENCES

11 APPENDIX A: THE Z TRANSFORMTHE Z TRANSFORM A.1 THE SAMPLED TIME DOMAIN AND THE Z TRANSFORM A.2 EXAMPLES A.3 APPROXIMATIONS IN GOING FROM THE FOURIER TO THE Z DOMAIN PROBLEM SET A REFERENCES

12 APPENDIX B: ANALYTIC SOLUTION TO CALCULATING THE ELECTRIC FIELDANALYTIC SOLUTION TO CALCULATING THE ELECTRIC FIELD REFERENCE

13 INDEX

14 END USER LICENSE AGREEMENT

1 Chapter 2Table 2.1 Properties of Human Muscle

2 Chapter 5Table 5.1 Breakdown of PML Parameters

3 Appendix ATable A.1 Some Z TransformsTable A.2 Properties of Z Transforms

1 Chapter 1 Figure 1.1 Interleaving of the E and H fields in space and time in the FDTD ... Figure 1.2 FDTD simulation of a pulse in free space after 100 time steps. Th... Figure 1.3 Simulation of an FDTD program with absorbing boundary conditions.... Figure 1.4 Simulation of a pulse striking dielectric material with a dielect... Figure 1.5 Simulation of a propagating sinusoidal wave of 700 MHz striking a... Figure 1.6 Simulation of a propagating sinusoidal wave striking a lossy diel...

2 Chapter 2Figure 2.1 Simulation of a pulse striking a dielectric medium with ε r=...Figure 2.2 (a) Relative dielectric constant and (b) conductivity as function...Figure 2.3 Simulation of a pulse striking a frequency‐dependent dielectric m...Figure 2.4 Simulation of a wave propagating in free space and striking a pla...Figure 2.5 Simulation of a wave propagating in free space and striking a pla...Figure 2.6 (a) Relative dielectric constant and (b) conductivity as function...

3 Chapter 3Figure 3.1 Interleaving of the E and H fields for the two‐dimensional TM for...Figure 3.2 Results of a simulation using the program fd2d_3_1.py. A Gaussian...Figure 3.3 Parameters related to the perfectly matched layer (PML).Figure 3.4 Results of a simulation using the program fd2d_3_2.py. A sinusoid...Figure 3.5 Total field/scattered field of the two‐dimensional problem space....Figure 3.6 Every point is in either the total field or the scattered field....Figure 3.7 Simulation of a plane wave pulse propagating in free space. The i...Figure 3.8 Simulation of a plane wave striking a dielectric cylinder. The fi...Figure 3.9 Simulation of a plane wave impinging on a dielectric cylinder. Th...Figure 3.10 Comparison of the FDTD results (solid lines) with the Bessel fun...

4 Chapter 4Figure 4.1 The Yee cell.Figure 4.2 A dipole antenna. The FDTD program specifies the metal arms of th...Figure 4.3 E zfield radiation from a dipole antenna in a three‐dimensional F...Figure 4.4 Radiation from a dipole antenna in an FDTD program with a seven‐poi...Figure 4.5 Total/scattered field in three dimensions.Figure 4.6 Total/scattered field boundary at k = ka .Figure 4.7 Comparison of the FDTD calculation (lines) with the Bessel functi...Figure 4.8 E zis calculated by the surrounding H xand H yvalues. The paramet...Figure 4.9 Comparison of the FDTD calculation (lines) with the Bessel functi...

5 Chapter 5Figure 5.1 Main program flow for fd3d_5_1.py.Figure 5.2 Window created using the Controllerclass. This displays the outp...

6 Chapter 6Figure 6.1 A diagram indicating the Sigma 60 applicator placed around the pa...Figure 6.2 Axial view of the Sigma 60 annular phased array.Figure 6.3 An illustration of the FDTD problem space containing the Sigma 60...Figure 6.4 FDTD model of the dipole antennas.Figure 6.5 The Hx field in front of the dipole is an indication of current f...Figure 6.6 The amplitude of the Fourier transform of Hx in front of the dipo...Figure 6.7 Illustration of the radiation from quadrant 1 for 300, 500, 600, ...Figure 6.8 Test configuration to evaluate the frequency response of the dipo...Figure 6.9 Output of the test illustrated in Fig. 6.5.Figure 6.10 Contour diagrams of the GAZ parameter illustrating how the patie...Figure 6.11 Flow chart of the treatment planning system.Figure 6.12 The operator specifies a target point (ipos,jpos) and the phases...Figure 6.13 The resulting SAR distributions for four different settings. The...

7 Appendix AFigure A.1 The response of Eq. (A.18) to a step function input, that is, x [ n

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2 Table of Contents

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