Computable scalar fields: A basis for PDE software

Haveraaen, Magne; Friis, Helmer André; Munthe-Kaas, Hans

doi:10.1016/j.jlap.2004.12.001

Cited by 11 publications

(8 citation statements)

References 17 publications

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“…The codes are implemented by the use of a flexible object-oriented programming environment, based on so called coordinate-free numerics (see e.g. [38][39][40]). …”

Section: Computational Examplesmentioning

confidence: 99%

A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids

Friis

Edwards

2011

Journal of Computational Physics

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“…The codes are implemented by the use of a flexible object-oriented programming environment, based on so called coordinate-free numerics (see e.g. [38][39][40]). …”

Section: Computational Examplesmentioning

confidence: 99%

A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids

Friis

Edwards

2011

Journal of Computational Physics

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“…The approach described in this paper will work equally well with an incomplete specification (though, it will of course not be able to test unspecified behaviour). Based on our experience developing and testing Sophus [HB05,HFMK05], we find such axioms useful.…”

Section: Axiom-based Testingmentioning

confidence: 99%

Testing with Axioms in C++ 2011.

Bagge¹,

David²,

Haveraaen³

2011

JOT

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Unit testing is an important part of modern software development, where individual code units are tested in isolation. Such tests are typically case-based, checking a likely error scenario or an error that has previously been identified and fixed. Coming up with good test cases is challenging, particularly when testing generic code, and focusing on individual tests can distract from creating tests that cover the full functionality.Concepts provide a generic way of describing code interfaces for generic code. Together with axioms, program behaviour can be specified algebraically in a formal or semi-formal way.In this paper we show how concepts and axioms can be expressed in standard C++ 2011, and explore how to generate generic unit tests, by treating the axioms as code to be evaluated with test data. We also show a generic way to generate test data for axiom-based testing in C++ 2011.

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“…In most cases we compare the solutions against the (nonsymmetric) triangular cellcentered MPFA O-method scheme presented in [2], in which the transmissibilities are evaluated in physical space with q = 1. The codes are implemented by the use of a flexible object-oriented programming environment, based on so-called coordinate-free numerics (see, e.g., [23,25,26]). In all cases we use unstructured triangular grids.…”

Section: Computational Examplesmentioning

confidence: 99%

Symmetric Positive Definite Flux-Continuous Full-Tensor Finite-Volume Schemes on Unstructured Cell-Centered Triangular Grids

Friis¹,

Edwards²,

Mykkeltveit³

2009

SIAM J. Sci. Comput.

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Novel cell-centered full-tensor finite-volume methods are presented for general unstructured grids in two spatial dimensions. The numerical schemes are flux-continuous and based on computing the transmissibilities in a local subcell transform space, ensuring that local flux matrices are symmetric. As a result the global discretization matrix is shown to be symmetric positive definite for any grid type. A symmetric physical space method is also introduced, and the symmetric methods are shown to be closely related. Discrete ellipticity conditions are derived for positive definiteness of the physical space and subcell space schemes. Computational examples are presented for unstructured triangular grids demonstrating good performance of the scheme. The schemes are compared with the so-called multipoint flux approximation (MPFA) O-method [I. Aavatsmark, T. Barkve, Good agreement between the methods is obtained, but the new scheme shows improved behavior in challenging cases.

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Computable scalar fields: A basis for PDE software

Cited by 11 publications

References 17 publications

A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids

A family of MPFA finite-volume schemes with full pressure support for the general tensor pressure equation on cell-centered triangular grids

Testing with Axioms in C++ 2011.

Symmetric Positive Definite Flux-Continuous Full-Tensor Finite-Volume Schemes on Unstructured Cell-Centered Triangular Grids

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