Verification of Computer Codes in Computational Science and Engineering: 1st Edition (Hardback) book cover

Verification of Computer Codes in Computational Science and Engineering

1st Edition

By Patrick Knupp, Kambiz Salari

Chapman and Hall/CRC

160 pages | 5 B/W Illus.

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pub: 2002-10-29
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Description

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

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

About the Series

Discrete Mathematics and Its Applications

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
COM053000
COMPUTERS / Security / General
MAT000000
MATHEMATICS / General
MAT021000
MATHEMATICS / Number Systems
MAT036000
MATHEMATICS / Combinatorics