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Advanced Computational Techniques and Numerical Solutions

Unlock Computational Mastery: Dive into the World of Functions, Equations, and Multigrid Methods! Discover the Power of Laplace, Wave Equations, and Parallel Computing in Our Comprehensive 39-Lecture Series. Transform Theory into Code with Practical Demos!

4.0 (19)

321 learners

What you'll learn

Understand the necessity and functionality of computers in problem-solving.
Apply numerical methods to represent functions and derivatives on computers.
Analyze the stability and convergence of solutions to Laplace and wave equations.
Implement advanced computational techniques like multigrid methods and parallel computing.

This course includes

32 hours of video
Certificate of completion
Access on mobile and TV

Course content

1 modules • 39 lessons • 32 hours of video

Advanced Computational Techniques and Numerical Solutions

39 lessons • 32 hours

▶

Mod-01 Lec-01 Introduction, Why and how we need computers47:54
Mod-01 Lec-02 Representing Arrays and functions on computers40:51
Mod-01 Lec-03 Representing functions - Box functions47:44
Mod-01 Lec-04 Representing functions - Polynomials & Hat functions53:34
Mod-01 Lec-05 Hat functions, Quadratic & Cubic representations50:27
Mod-01 Lec-06 Demo - Hat functions, Aliasing50:57
Mod-01 Lec-07 Representing Derivatives - finite differences50:44
Mod-01 Lec-08 Finite differences, Laplace equation49:31
Mod-01 Lec-09 Laplace equation - Jacobi iterations50:12
Mod-01 Lec-10 Laplace equation - Iteration matrices51:17
Mod-01 Lec-11 Laplace equation - convergence rate33:00
Mod-01 Lec-12 Laplace equation - convergence rate Continued30:22
Mod-01 Lec-13 Demo - representation error, Laplace equation50:56
Mod-01 Lec-14 Demo - Laplace equation, SOR50:55
Mod-01 Lec-15 Laplace equation - final, Linear Wave equation51:24
Mod-01 Lec-16 Linear wave equation - Closed form & numerical solution, stability analysis50:45
Mod-01 Lec-17 Generating a stable scheme & Boundary conditions51:33
Mod-01 Lec-18 Modified equation51:11
Mod-01 Lec-19 Effect of higher derivative terms on Wave equation51:33
Mod-01 Lec-20 Artificial dissipation, upwinding, generating schemes51:47
Mod-01 Lec-21 Demo - Modified equation, Wave equation51:05
Mod-01 Lec-22 Demo - Wave equation / Heat Equation50:02
Mod-01 Lec-23 Quasi-linear One-Dimensional. wave equation31:31
Mod-01 Lec-24 Shock speed, stability analysis, Derive Governing equations51:49
Mod-01 Lec-25 One-Dimensional Euler equations - Attempts to decouple51:06
Mod-01 Lec-26 Derive Eigenvectors, Writing Programs52:14
Mod-01 Lec-27 Applying Boundary conditions50:53
Mod-01 Lec-28 Implicit Boundary conditions51:11
Mod-01 Lec-29 Flux Vector Splitting, setup Roe’s averaging51:13
Mod-01 Lec-30 Roe’s averaging51:58
Mod-01 Lec-31 Demo - One Dimensional flow51:33
Mod-01 Lec-32 Accelerating convergence - Preconditioning, dual time stepping52:40
Mod-01 Lec-33 Accelerating convergence, Intro to Multigrid method53:33
Mod-01 Lec-34 Multigrid method53:31
Mod-01 Lec-35 Multigrid method - final, Parallel Computing52:15
Mod-01 Lec-36 Calculus of Variations - Three Lemmas and a Theorem52:36
Mod-01 Lec-37 Calculus of Variations - Application to Laplace Equation50:55
Mod-01 Lec-38 Calculus of Variations -final & Random Walk52:39
Mod-01 Lec-39 Overview and Recap of the course53:46

finite differences

Laplace equation

wave equation

convergence rate

multigrid method

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