Assessing the Reliability of Complex Models Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification (2012) / Chapter Skim
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3 Verification
3 Verification
Pages 31-36
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From page 31... ...
This includes code verification (determining whether the code correctly implements the intended algorithms) and solution verification (determining the accuracy with which the algorithms solve the mathematical model's equations for specified quantities of interest [QOIs]
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From page 32... ...
solutions allows researchers to assess, for example, the degree to which code implementation achieves the expected solution to the mathematical system of equations. Because the reference solution is exact and the code implements numerical approximation to the exact solution, one can test convergence rates against those predicted by theory.
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From page 33... ...
Uncertainty quantification studies explore a broad variety of input parameters, which may result in unexpected results from algorithms and physics models, even those that have undergone extensive testing. Some software development teams have found utility in employing static analysis tools, including those that incorporate logic-checking algorithms, for source code checking (Ayewah et al., 2008)
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From page 34... ...
Solution verification is a matter of numerical-error estimation, the goal being to estimate the error present in the computational QOI relative to an exact QOI from the underlying mathematical model. While code verification considers generic formulations of simplified problems within a class that the code was designed to treat, solution verification pertains to the specific, large-scale modeling problem that is at the center of the simulation effort, with specific inputs (boundary and initial conditions, constitutive parameters, solution domains, source terms)
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From page 35... ...
Finding: Methods exist for estimating tight two-sided bounds for numerical error in the solution of linear elliptic PDEs. Methods are lacking for similarly tight bounds on numerical error in more complicated problems, including those with nonlinearities, coupled physical phenomena, coupling across scales, and stochasticity (as in stochastic PDEs)
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From page 36... ...
2001. An Optimal Control Approach to a Posteriori Error Estimation in Finite Element Methods.
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