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.
Author(s): Patrick Knupp, Kambiz Salari
Edition: 1
Publisher: Chapman and Hall/CRC
Year: 2002
Language: English
Pages: 160
Cover......Page 1
Half Title......Page 2
Title......Page 4
Copyright......Page 5
Preface......Page 6
Contents......Page 10
List of Illustrations......Page 14
List of Tables......Page 16
chapter one Introduction to code verification......Page 18
chapter two The mathematical model and numerical algorithm......Page 24
chapter three The order-verification procedure (OVMSP)......Page 36
chapter four Design of coverage test suite......Page 52
chapter five Finding exact solutions......Page 58
chapter six Benefits of the order verification procedure......Page 76
chapter seven Related code-development activities......Page 86
chapter eight Sample code-verification exercises......Page 92
chapter nine Advanced topics......Page 106
chapter ten Summary and conclusions......Page 116
appendix I Other methods for PDE code testing......Page 124
appendix II Implementation issues in the forward approach......Page 128
appendix III Results of blind tests......Page 130
appendix IV A manufactured solution to the free-surface porous media equations......Page 150
Index......Page 154
