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MASA : a library for verification using manufactured and analytical solutions

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Abstract

In this paper we introduce the Manufactured Analytical Solution Abstraction ( MASA ) library for applying the method of manufactured solutions to the verification of software used for solving a large class of problems stemming from numerical methods in mathematical physics including nonlinear equations, systems of algebraic equations, and ordinary and partial differential equations. We discuss the process of scientific software verification, manufactured solution generation using symbolic manipulation with computer algebra systems such as Maple™ or SymPy, and automatic differentiation for forcing function evaluation. We discuss a hierarchic methodology that can be used to alleviate the combinatorial complexity in generating symbolic manufactured solutions for systems of equations based on complex physics. Finally, we detail the essential features and examples of the Application Programming Interface behind MASA , an open source library designed to act as a central repository for manufactured and analytical solutions over a diverse range of problems.

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Notes

  1. http://pecos.ices.utexas.edu.

  2. The workstation used in this work was a 6-core 3.3 GHz i7 Intel processor with 12 GB RAM running Ubuntu Linux.

  3. https://red.ices.utexas.edu/projects/software. Please note that the server certification fingerprint requires a modern web browser.

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Acknowledgments

This material is based in part upon work supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615]. Algebraic manipulations for generating source terms in this paper were performed using Maple™ and SymPy. We appreciate the many interesting discussions with the other staff and faculty of the PECOS project. We are particularly grateful to Onkar Sahni for the many helpful comments during the development of MASA .

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Authors and Affiliations

  1. Predictive Engineering and Computational Sciences Center, Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, 78712, USA

    Nicholas Malaya, Kemelli C. Estacio-Hiroms, Roy H. Stogner, Karl W. Schulz, Paul T. Bauman & Graham F. Carey

Authors
  1. Nicholas Malaya
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  2. Kemelli C. Estacio-Hiroms
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  3. Roy H. Stogner
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  4. Karl W. Schulz
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  5. Paul T. Bauman
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  6. Graham F. Carey
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Corresponding author

Correspondence to Nicholas Malaya.

Additional information

The authors wish to dedicate this paper to the memory of Professor Graham Carey, who passed away during preparation of this work. Professor Carey was a mentor and advisor to the authors of this paper and will be greatly missed.

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Malaya, N., Estacio-Hiroms, K.C., Stogner, R.H. et al. MASA : a library for verification using manufactured and analytical solutions. Engineering with Computers 29, 487–496 (2013). https://doi.org/10.1007/s00366-012-0267-9

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  • DOI: https://doi.org/10.1007/s00366-012-0267-9

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