Verification of Computer Codes in Computational Science and Engineering

Patrick Knupp, Kambiz Salari

• Publisher: Chapman and Hall/CRC
• Year: 2002
• Print ISBN: 9780367838157
• eBook ISBN: 9781420035421
• Edition: 1
• Topic: Computer Science
• Subtopic: Cyber Security
• Index: Computer Science

How can one be assured that computer codes that solve differential equations are correct? Standard practice using benchmark testing no longer provides full coverage because today's production codes solve more complex equations using more powerful algorithms. By verifying the order-of-accuracy of the numerical algorithm implemented in the code, one can detect most any coding mistake that would prevent correct solutions from being computed.

Verification of Computer Codes in Computational Science and Engineering sets forth a powerful alternative called OVMSP: Order-Verification via the Manufactured Solution Procedure. This procedure has two primary components: using the Method of Manufactured Exact Solutions to create analytic solutions to the fully-general differential equations solved by the code and using grid convergence studies to confirm the order-of-accuracy. The authors present a step-by-step procedural guide to OVMSP implementation and demonstrate its effectiveness.

Properly implemented, OVMSP offers an exciting opportunity to identify virtually all coding 'bugs' that prevent correct solution of the governing partial differential equations. Verification of Computer Codes in Computational Science and Engineering shows you how this can be done. The treatment is clear, concise, and suitable both for developers of production quality simulation software and as a reference for computational science and engineering professionals.

Table of contents

• Preface
• Contents
• List of Illustrations
• List of Tables
• chapter one Introduction to code verification
• chapter two The mathematical model and numerical algorithm
• chapter three The order-verification procedure (OVMSP)
• chapter four Design of coverage test suite
• chapter five Finding exact solutions
• chapter six Benefits of the order verification procedure
• chapter seven Related code-development activities
• chapter eight Sample code-verification exercises
• chapter nine Advanced topics
• chapter ten Summary and conclusions
• appendix I Other methods for PDE code testing
• appendix II Implementation issues in the forward approach
• appendix III Results of blind tests
• appendix IV A manufactured solution to the free-surface porous media equations
• Index