Basic Multigrid Solvers

Computationally efficient solutions to sparse systems of linear equations.

4.50 (13 reviews)
Udemy
platform
English
language
Engineering
category
instructor
Basic Multigrid Solvers
138
students
1 hour
content
Jan 2021
last update
$39.99
regular price

What you will learn

Basics of multigrid solvers for large, sparse systems of linear equations.

Description

Multigrid techniques are used in most commercial computational fluid dynamics codes where large numbers of unknowns are common.  The techniques are used to accelerate convergence of basic iterative methods using multiple grid levels.  In this course we apply basic multigrid techniques to one- and two-dimensional elliptic problems discretized using a finite-difference method.  The approach may be extended to the finite-volume and other methods, or may be applied to general sparse linear systems of the form Ax=b.  The one- and two-dimensional codes are written in Fortran90 and source codes available for download.  Prospective students should be familiar with basic numerical methods and be proficient in a scientific programming language.

Content

Multigrid Methods

Introduction
Download Notes and Codes
Jacobi Iterative Technique
Gauss-Seidel Iterative Technique
Jacobi and Gauss-Seidel Error Reduction
Quiz1
Multigrid Basics
Prototype One Dimensional Problem
One Dimensional Results
Options and Terminology
Two Dimensional Results

One-Dimensional Multigrid Code

One Dimensional Code Subroutines
One-Dimensional Code Main Program
One-Dimensional Code Demonstration

Two-Dimensional Multigrid Code

Two-Dimensional Code
Two-Dimensional Code Demonstration

Reviews

Ilija
July 1, 2021
This is a great course! It thoroughly explains multigrid methods for solving differential equations. The presentation is clear and easy to follow. After finishing this course one gets a good understanding of prolongation and restriction schemes, different multigrid cycles, and various parameters one can adjust to optimize convergence.

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3717952
udemy ID
12/21/2020
course created date
1/22/2021
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