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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.
Fundamentals of Grid Generation is an outstanding text/reference
designed to introduce students in applied mathematics, mechanical
engineering, and aerospace engineering to structured grid
generation. It provides excellent reference material for
practitioners in industry, and it presents new concepts to
researchers. Readers will learn what boundary-conforming grids are,
how to generate them, and how to devise their own methods.
The text is written in a clear, intuitive style that doesn't get
bogged down in unnecessary abstractions. Topics covered include
planar, surface, and 3-D grid generation; numerical techniques;
solution adaptivity; the finite volume approach to discretization
of hosted equations; concepts from elementary differential
geometry; and the transformation of differential operators to
general coordinate systems. The book also reviews the literature on
algebraic, conformal, orthogonal, hyperbolic, parabolic, elliptic,
biharmonic, and variational approaches to grid generation. This
unique volume closes with the author's original methods of
variational grid generation.
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