List of Figures

• 4.1. Triangular element.
• 4.2. Barycentric coordinates outside a triangular element.
• 4.3. Two-dimensional domain transformation.
• 4.4. Node and element numbering in a discretized domain.
• 4.5. Homogeneous Neumann boundary conditions on the outer boundary.
• 4.6. The outer region is cut off.
• 4.7. Tetrahedral element.
• 4.8. Three-dimensional domain transformation.
• 5.1. The inductor inside the simulation domain in Fig. <5.2>.
• 5.2. The entire simulation domain.
• 5.3. Inside view of the simulation domain in Fig. <5.2>.
• 5.4. The conductor entry.
• 5.5. The shape function along Edge $12$ .
• 5.6. The shape function along Edge $34$ .
• 5.7. The sum of all shape functions in the tetrahedron.
• 5.8. The shape function along Edge $12$ .
• 5.9. The sum of the shape functions in the triangle.
• 6.1. The simulated coaxial structure.
• 6.2. Current density distribution.
• 6.3. Magnetic field.
• 6.4. Current density distribution at low frequency.
• 6.5. Current density distribution at $3$ GHz.
• 6.6. Current density distribution at $30$ GHz.
• 6.7. Current density distribution at $300$ GHz.
• 6.8. Magnetic field distribution at low frequency.
• 6.9. Magnetic field distribution at $3$ GHz.
• 6.10. Magnetic field distribution at $30$ GHz.
• 6.11. Magnetic field distribution at $300$ GHz.
• 6.12. The simulation domain.
• 6.13. The generated mesh.
• 6.14. Surface view of the current density [A/m$^2$ ] distribution at $100$ MHz.
• 6.15. Surface view of the current density [A/m$^2$ ] distribution at $10$ GHz.
• 6.16. Current density distribution at $1$ GHz.
• 6.17. Magnetic field distribution [A/m] at $1$ GHz.
• 6.18. Current density distribution in the via at $100$ MHz.
• 6.19. Current density distribution in the via at $10$ GHz.
• 6.20. Current density [A/m$^2$ ] distribution in the substrate at $1$ GHz.
• 6.21. Magnetic field [A/m] in the substrate at $1$ GHz.
• 6.22. An interconnect bus.
• 6.23. The simulation area.
• 6.24. The electrodes in the simulation area.
• 6.25. The electric potential distribution with x periodicity.
• 6.26. The iso faces of the electric potential distribution with x periodicity.
• 6.27. The electric potential distribution without periodicity.
• 6.28. The iso faces of the electric potential distribution without periodicity.
• A.1. Two-dimensional domain transformation.