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Browse materialsMIT 6.336J · Fall 2003

Introduction to Numerical Simulation (SMA 5211)

Subject: Mechanical Engineering

Art: Palmer, Edward, 1803-1872, Figures 113-123. Plate Electrical Machines, 1840 · Public domain

Instructors: Prof. Jacob White, Prof. Jaime Peraire, Prof. Luca Daniel, Prof. Nicholas Hadjiconstantinou, Prof. Anthony T. Patera
Term: Fall 2003
Level: Graduate
What's inside: 1 lecture note · 79 other files · 3 web pages
Materials open: MIT OCW

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Source: MIT OpenCourseWare 6.336J Introduction to Numerical Simulation (SMA 5211), Fall 2003, Prof. Jacob White, Prof. Jaime Peraire, Prof. Luca Daniel, Prof. Nicholas Hadjiconstantinou, Prof. Anthony T. Patera — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

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Lecture Notes

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48 files

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9 files

MIT OpenCourseWare, Prof. Jacob White, Prof. Jaime Peraire, Prof. Luca Daniel, Prof. Nicholas Hadjiconstantinou, Prof. Anthony T. Patera, 6.336J Introduction to Numerical Simulation (SMA 5211), Fall 2003.

License: CC BY-NC-SA 4.0 · Edition: Fall 2003 · Open the original course on OCW ↗

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Introduction to Numerical Simulation (SMA 5211)

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Assignments

Other materials from this course

Lecture 1: Example Problems and Basic Equations

Lecture 2: Equation Formulation Methods - Stamping Techniques, Nodal versus Node-Branch Form

Lecture 3: Linear System Solution - Dense GE, Conditioning, Stability

Lecture 4: Direct Methods for Sparse Linear Systems - Data Structures, Fill-in, Ordering, Graph Interpretations

Lecture 5: Linear System Solution - Orthogonalization Methods, QR, Singular Matrices

Lecture 6: QR and Krylov Iterative Methods. Brief Convergence Analysis.

Lecture 7: Krylov Methods (cont.)

Lecture 8: Nonlinear System Solution - 1D Newton Methods, Convergence Analysis

Lecture 9: Nonlinear System Solution-Multi-D Newton, Forming Jacobian by Stamping Approach, Singularity

Lecture 10: Nonlinear System Solution - Damping, Optimization and Continuation Schemes

Lecture 11: Nonlinear System Solution - Matrix-Implicit Methods and Methods for Singular Problems

Lecture 12: ODE Solution Methods - BE, FE, Trap Examples, Convergence

Lecture 13: ODE Solution Methods - Multistep Methods and Stability, Runga-Kutta Methods

Lecture 14: ODE Solution Methods - Stiffly Stable and Conservative Schemes

Lecture 15: Time-Periodic Solution Methods - Finite-Difference and Shooting Methods

Lecture 16: Time-Periodic Solution Methods - Matrix-Implicit Algorithms and Preconditioning

Lecture 17: Molecular Dynamics - Basic Numerical Issues

Lecture 18: Molecular Dynamics (cont.)

Lecture 19: 3-D Elliptic Problems - F-D Methods, Error Estimation

Lecture 20: 3-D Elliptic Problems - Finite-Element and Spectral Methods

Lecture 21: 3-D Elliptic Problems - FFT and Multigrid Methods

Lecture 22: 3-D Elliptic Problems - Boundary-Element Approach

Lecture 23: 3-D Elliptic Problems - FFT and Multipole Methods

Lecture 24: Model Order Reduction I

Lecture 25: Model Order Reduction II

Lecture 26: Class Choice