1. Introduction.- 1.1 Modeling of MOS Devices.- 1.2 Parasitic Models.- 1.3 Background from Algebra.- 1.4 Background from Analysis.- 1.5 Overview of the Book.- 2. Boundary Value Problems in VLSI Modeling.- 2.1 Field Equations.- 2.2 Integral Equations: the MOSFET Case.- 2.3 Integral Equations: Parasitic Capacitance.- 3. Green's Function for Stratified Media.- 3.1 Definition.- 3.2 The Bounded Multilevel Dielectric Problem.- 3.3 The Unbounded Multilevel Dielectric Problem.- 4. Galerkin Boundary Finite Elements.- 4.1 Element and Local Shape Function.- 4.2 An Optimal Solution.- 4.3 Reduction Using Constraints.- 4.4 Evaluation of Green's Function Integrals.- 4.5 Determination of the Number of Terms Required for Green's Function.- 4.6 Results and Comparisons.- 5. Point Collocation and Further Simplifications.- 5.1 Point Collocation.- 5.2 Further Reduction of Point-Collocation Integrals.- 5.3 The Capacitance Matrix.- 6. Reduced Models.- 6.1 Preliminaries.- 6.2 The Generalized Schur Algorithm.- 6.3 Approximation Theory and Error Analysis.- 6.4 Architectures.- 7. Hierarchical Reduced Models.- 7.1 Two Dimensional Ordering.- 7.2 Hierarchical Approximants.- 7.3 The Sparse Inverse Approximation.- 8. On the Modeling of a Short-channel MOSFET below Threshold.- 8.1 Analytical Solution of the Poisson Equation.- 8.2 Boundary Conditions.- 8.3 Discussion.- 9. Parasitic Capacitances and their Linear Approximation.- 9.1 Parallel Conductors.- 9.2 Corners.- 9.3 Crossing Strips.- 9.4 Combination of Corner and Crossing Strips.- 10. Interconnection Resistances.- 10.1 Introduction.- 10.2 Finite Element Method.- 10.3 The Boundary Finite Element Method.- 11. Hybrid Finite Elements.- 11.1 Introduction.- 11.2 Direct Hybrid Field Modeling.- 11.3 Extension to the Poisson Case.- 11.4 Using a Scattered Field.- 12. Appendices.- 12.1 Appendix 3.1: Solution of Equation (3.8).- 12.2 Appendix 3.2: Fourier Integral Evaluation.- 12.3 Appendix 4.1: Evaluation of Singular Integrals.- 12.4 Appendix 4.2: Derivation of (4.41).- 12.5 Appendix A.5.