1. Introduction
a. examples of problems
i. electrical
ii.thermal
iii.structural
2. Equation formulation
a. nodal
b. modified nodal
c. sparse tableau analysis
3. Gaussian elimination
a. pivoting and conditioning
4. Sparse matrix methods and data structures
5. QR and Generalized Conjugant Residual methods
a. GCR convergence and preconditioning
b. Krylov methods
6.
a. modifications, and
b. convergence
7. Solution of ordinary differential equations
a. multi-step methods
i.convergence
ii.consistency
iii.stability
8. Adjoint equations
a. computations of sensitivities
9. Simulation of discrete systems
a. event driven versus compiled code methods
b. random inputs with constraints
c. targeting particular objectives
10. Periodic steady state solutions
a. time domain
b. spectral methods
11. Integral equations
a. simulation of package, signal lines and MEMS
b. Poisson and Laplace equations
c. exterior and interior methods
d. collocation and Galerkin methods
12. Hierarchical methods
13. Finite element methods
a. Hat basis functions
b. Galerkin methods
14. Boundary value problems and finite differences
a. 2D and 3D problems
15. Model order reduction
a. Eigenmode analysis
b. rational function matching
c. moment matching