1

Example Problems and Basic Equations (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Luca Daniel, Shihhsien Kuo, and Karen Veroy.)

2

Equation Formulation Methods - Stamping Techniques, Nodal versus Node-Branch Form (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

3

Linear System Solution - Dense GE, Conditioning, Stability (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

4

Direct Methods for Sparse Linear Systems - Data Structures, Fill-in, Ordering, Graph Interpretations (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Luca Daniel, and Karen Veroy.)

5

Linear System Solution - Orthogonalization Methods, QR, Singular Matrices (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

6

QR and Krylov Iterative Methods. Brief Convergence Analysis (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

7

Krylov Methods (cont.) (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

8

Nonlinear System Solution - 1D Newton Methods, Convergence Analysis (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.)

9

Nonlinear System Solution-Multi-D Newton, Forming Jacobian by Stamping Approach, Singularity (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.)

10

Nonlinear System Solution - Damping, Optimization and Continuation Schemes (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.)

11

Nonlinear System Solution - Matrix-Implicit Methods and Methods for Singular Problems (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, Jaime Peraire, and Andrew Lumsdaine.)

12

ODE Solution Methods - BE, FE, Trap Examples, Convergence (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Jaime Peraire.)

13

ODE Solution Methods - Multistep Methods and Stability, Runga-Kutta Methods (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

14

ODE Solution Methods - Stiffly Stable and Conservative Schemes (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

15

Time-Periodic Solution Methods - Finite-Difference and Shooting Methods (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

16

Time-Periodic Solution Methods - Matrix-Implicit Algorithms and Preconditioning (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

17

Molecular Dynamics - Basic Numerical Issues (PDF)(Courtesy of Nicolas Hadjiconstantinou.)

18

Molecular Dynamics (cont.) (PDF) (Courtesy of Nicolas Hadjiconstantinou.)

19

3-D Elliptic Problems - F-D Methods, Error Estimation (PDF) (Courtesy of Jaime Peraire, Anthony Patera, Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Dimitrios Rovas.)

20

3-D Elliptic Problems - Finite-Element and Spectral Methods (PDF) (Courtesy of Jaime Peraire.)

21

3-D Elliptic Problems - FFT and Multigrid Methods (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

22

3-D Elliptic Problems - Boundary-Element Approach (PDF) (Courtesy of Deepak Ramaswamy, Michal Rewienski, Karen Veroy, and Xin Wang.)

23

3-D Elliptic Problems - FFT and Multipole Methods (PDF - 4.0 MB) (Courtesy of Deepak Ramaswamy, Michal Rewienski, and Karen Veroy.)

24

Model Order Reduction I

25

Model Order Reduction II

Problem Set 1 (PDF)

loadmatrix.m (M), readckt.m (M), readelement.m (M), test.ckt (CKT), test2.ckt (CKT), test3.ckt (CKT)

Problem Set 2 (PDF)

qr_.m (M)

Problem Set 3 (PDF)

qr_.m (M)

Problem Set 4 (PDF)

pois2d.m (M), sgcr.m (M), tgcr.m (M)

Problem Set 5 (PDF)

Problem Set 6 (PDF)

force.m (M), loadnewton.m (M), newton.m (M), readjoint.m (M), readload.m (M), readsystem.m (M), test1.sys (SYS), test2.sys (SYS), test3.sys (SYS), test4.sys (SYS), test5.sys (SYS), test6.sys (SYS), test7.sys (SYS), test8.sys (SYS), test9.sys (SYS), test10.sys (SYS), test11.sys (SYS)

Problem Set 7 (PDF)

Problem Set 8 (PDF)

calccap.m (M), calcp.m (M), collocation.m (M), gencolloc.m (M), plate144.qif (QIF), plate36.qif (QIF), plate9.qif (QIF), plotpanels.m (M), readpanel.m (M), readpanels.m (M), sphere192.qif (QIF), sphere48.qif (QIF), sphere768.qif (QIF)

Moldy molecular dynamics program