[CFD] Conjugate Gradient for CFD (Part 1): Background and Steepest Descent

An introduction to the conjugate gradient method and other gradient descent based methods (steepest descent method) for CFD. This is Part 1 of a 2 Part lecture series. Time stamps 0:00 Introduction 2:53 Gauss-Seidel Recap 7:20 Quadratic Form 14:48 Gradient of f 19:37 Finding the minimum 24:00 General algorithm 25:53 Steepest descent method 29:50 Search direction (pk) 32:25 Search distance (alphak) 39:55 Steepest descent summary 41:33 Conjugate gradient motivation 43:02 Summary 44:33 Outro References J. Shewchuk 'An Introduction to the Conjugate Gradient Method Without the Agonizing Pain', Edition 1 1/4, 1994. https://www.cs.cmu.edu/~quake-papers/... ============================================ Want to learn more? ============================================ Grab a copy of my CFD Fundamentals Course (for beginners): https://www.udemy.com/course/computat... Learn how to write your own CFD code in MATLAB and python (for intermediates): https://dr-aidan-wimshurst-s-school.t... Learn how I draw my figures and diagrams in Inkscape (for everyone): https://dr-aidan-wimshurst-s-school.t... ============================================ Did you like the video? ============================================ Download the lecture slides from my website: https://www.fluidmechanics101.com/pag... Buy me a coffee to say thanks: https://www.buymeacoffee.com/NKEZrhvg0 Support the channel on Patreon (and get useful extras for your CFD studies):   / fluidmechanics101   ============================================ Donations: ============================================ 1) PayPal https://www.paypal.me/fluidmechanics101 ================================== Disclaimer ================================== The methods, algorithms, equations, formulae, diagrams and explanations in this talk are for educational and demonstrative purposes only. They should never be used to analyse, design, accredit or validate real scientific / engineering / mathematical structures and flow systems. For such applications, appropriate trained, qualified and accredited (SQEP) engineers / scientists should be consulted along with the appropriate documentation, procedures and engineering standards. Furthermore, the information contained within this talk has not been verified, peer reviewed or checked in any way and is likely to contain several errors. It is therefore not appropriate to use this talk itself (or any of the algorithms, equations, formulae, diagrams and explanations contained within this talk) as an academic or technical reference. The reader should consult the original references and follow the verification and validation processes adopted by your company / institution when carrying out engineering calculations and analyses. Fluid Mechanics 101 and Dr. Aidan Wimshurst are not accountable or liable in any form for the use or misuse of the information contained in this talk beyond the specific educational and demonstrative purposes for which it was intended.