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Verification of Computer Codes in Computational Science and Engineering

Verification of Computer Codes in Computational Science and Engineering by Patrick Knupp
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INTRODUCTION TO CODE VERIFICATION
THE MATHEMATICAL MODEL AND NUMERICAL ALGORITHM
The Mathematical Model
Numerical Methods for Solving Differential Equations
THE CODE VERIFICATION PROCEDURE
Static Testing
Dynamic Testing
Overview of the Order-Verification Procedure
Details of the Procedure
Closing Remarks
DESIGN OF COVERAGE TEST SUITE
Basic Design Issues
Coverage Issues Related to Boundary Conditions
Coverage Issues Related to Grids and Grid Refinement
FINDING EXACT SOLUTIONS
Obtaining Exact Solutions from the Forward Problem
The Method of Manufactured Exact Solutions
BENEFITS OF THE ORDER-VERIFICATION PROCEDURE
A Taxonomy of Coding Mistakes
A Simple PDE Code
Blind Tests
RELATED CODE DEVELOPMENT ACTIVITIES
Numerical Algorithm Development
Testing for Code Robustness
Testing for Code Efficiency
Code Confirmation Exercises
Solution Verification
Code Validation
Software Quality Engineering
SAMPLE CODE VERIFICATION EXERCISES
Burgers' Equation in Cartesian Coordinates (Code 1)
Burgers' Equation in Curvilinear Coordinates (Code 2)
Incompressible Navier-Stokes (Code 3)
Compressible Navier-Stokes (Code 4)
ADVANCED TOPICS
Computer Platforms
Look-up Tables
Automatic Time-Stepping Options
Hard-Wired Boundary Conditions
Codes with Artificial Dissipation Terms
Eigenvalue Problems
Solution Uniqueness
Solution Smoothness
Codes with Shock Capturing Schemes
Dealing with Codes that Make Non-Ordered Approximations
SUMMARY AND CONCLUSIONS
REFERENCES
APPENDICES
Other Methods for PDE Code Testing
Implementation Issues in the Forward Approach
Results of Blind Tests
A Manufactured Solution to the Free-Surface Porous Media Equations
INDEX
CRC Press; October 2002
161 pages; ISBN 9781420035421
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Title: Verification of Computer Codes in Computational Science and Engineering
Author: Patrick Knupp; Kambiz Salari
 
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