Basic Multigrid Solvers

What you'll learn
Basics of multigrid solvers for large, sparse systems of linear equations.
Requirements
Background in a scientific programming language and an understanding of basic numerical methods for solving linear systems.
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.
Overview
Section 1: Multigrid Methods
Lecture 1 Introduction
Lecture 2 Download Notes and Codes
Lecture 3 Jacobi Iterative Technique
Lecture 4 Gauss-Seidel Iterative Technique
Lecture 5 Jacobi and Gauss-Seidel Error Reduction
Lecture 6 Multigrid Basics
Lecture 7 Prototype One Dimensional Problem
Lecture 8 One Dimensional Results
Lecture 9 Options and Terminology
Lecture 10 Two Dimensional Results
Section 2: One-Dimensional Multigrid Code
Lecture 11 One Dimensional Code Subroutines
Lecture 12 One-Dimensional Code Main Program
Lecture 13 One-Dimensional Code Demonstration
Section 3: Two-Dimensional Multigrid Code
Lecture 14 Two-Dimensional Code
Lecture 15 Two-Dimensional Code Demonstration
Users of commercial CFD solvers who would like some background on multigrid techniques used in the codes. Upper division undergraduates and beginning level graduate students in science and engineering.


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