Lecture 14: What we learnt
Higher Order Finite Difference Approximations
Cylindrical Coordinate System
Governing equations
Derivation of finite difference equations
Application of boundary conditions
1
Lecture 15: What we will learn
Mid-term Exam Di

Lecture 1: What we will learn
Why is engineering analysis important?
What are the main steps in engineering analysis?
Verification and Validation
Sanity Checks
Essentials of MECHENG 6507
What it teaches you
What it does not teach you
Classificatio

Lecture 13: What we learnt
Algebraic Multi-Grid Method
Review of Linear Algebraic Equation Solvers
1
Lecture 14: What we will learn
Higher Order Finite Difference Approximations
Cylindrical Coordinate System
Governing equations
Derivation of finite

Lecture 15: What we learnt
Mid-term Exam Discussion
Cylindrical Coordinate System
Application of boundary conditions continued
Treatment of Time Derivative
Explicit (or Forward Euler) Method
1
Lecture 16: What we will learn
Stability Analysis of the

Lecture 12: What we learnt
Geometric Multi-Grid Method
Basic philosophy
Formulation and Algorithm
1
Lecture 13: What we will learn
Algebraic Multi-Grid Method
Review of Linear Algebraic Equation Solvers
2
Iterative Solvers
Iterative solvers may be broa

Lecture 8: What we learnt
Review of Matrix Operations
Method of Steepest Descent
Conjugate Gradient (CG) Method
1
Lecture 9: What we will learn
Important Practices in Coding for MSD and CG Method
Variations of the CG Method
Bi-Conjugate Gradient (BC

Lecture 11: What we learnt
Stability Analysis of Iterative Methods
1D Advection-Diffusion with GS iterations
Effect of Inertial Damping on Spectral Radius
2D Diffusion Equation with GS and ADI
1
Lecture 12: What we will learn
Geometric Multi-Grid Meth

Lecture 7: What we learnt
Stones Strongly Implicit Method
1
Lecture 8: What we will learn
Review of Matrix Operations
Method of Steepest Descent
Conjugate Gradient (CG) Method
2
Iterative Solvers
Iterative solvers may be broadly classified as:
Point-

Lecture 10: What we learnt
Stability and Convergence
Iteration/Amplification matrix
Stability criterion
Spectral radius of convergence
Review of Fourier Series
Fourier Analysis of Errors
Calculation of Spectral Radius of Convergence
Basic procedur

Lecture 9: What we learnt
Important Practices in Coding for MSD and CG Method
Variations of the CG Method
Bi-Conjugate Gradient (BCG) Method
Conjugate Gradient Squared (CGS) Method
Generalized Minimum Residual (GMRES) Method
Summary of Errors
Purpo

Lecture 1: What we learnt
Why is engineering analysis important?
What are the main steps in engineering analysis?
Verification and Validation
Sanity Checks
Essentials of MECHENG 6507
What it teaches you
What it does not teach you
Classification of

Lecture 4: What we learnt
Treatment of Non-Linear Source Terms
Residuals and Convergence
Newtons Method for System of Non-Linear Equations
1
Lecture 5: What we will learn
Finite Difference Method in 2D
Iterative Solvers
Jacobi Method
Gauss-Seidel M

Lecture 5: What we learnt
Finite Difference Method in 2D
Iterative Solvers
Jacobi Method
Gauss-Seidel Method
1
Lecture 6: What we will learn
Iterative Solvers
Alternating Direction Implicit (ADI) Method
Condition Number and its Implications
Pre-Co

Lecture 2: What we learnt
Overview of Methods for Solving PDEs
Overview of Types of Meshes
The Finite Difference Method (FDM)
Procedure for derivation of discrete equations
1
Lecture 3: What we will learn
The Finite Difference Method (FDM)
Applicati

Lecture 3: What we learnt
The Finite Difference Method (FDM)
Application of various types of Boundary Conditions
Direct Solution of a set of Linear Algebraic Equations
Gaussian Elimination
Tri-Diagonal Matrix System
1
Lecture 4: What we will learn
T

Lecture 6: What we learnt
Iterative Solvers
Alternating Direction Implicit (ADI) Method
Condition Number and its Implications
Pre-Conditioning
Correction Form of Equations and Inertial Damping
1
Lecture 7: What we will learn
Stones Strongly Implicit