In order to validate a numerical code. I compute benchmark tests. I don't know that I should make other experiment tests or the benchmark tests are enough to validate our numerical model.
Hi Hamdi,
I recommend the following reference on the subject and encourage you to adopt the good practices that are discussed herein:
- Wilson et al., "Best Practices for Scientific Computing", 2012 - http://www.ee.columbia.edu/~dpwe/e6891/resources/1210.0530v3.pdf
Regards
It is customary to exercise both (Verification & Validation) in order to sure. Experimental results are needed to Validate, if available. You already did Verification part.
Benchmark validation is a great first step, but it is no guarantee.
In my numerical computations (computational physics), I always try additional tests of limiting cases, when one or more parameters are set to extreme values for which the outcome (or at least the limiting trend of the outcome) can be estimated analytically (or in some way independent of the numerical code in question).
For instance:
- I might try the low or high frequency limit for acoustic, electromagnetic or seismic wave radiation models for instance, or the long-range limit, or the long time duration limit.
- When solving partial differential equations (PDEs) numerically, I might do checks that boundary conditions and the PDEs are satisfied in any given solution.
- For the numerical computation of special functions (e.g., Airy functions, modified Bessel functions of fractional order and complex argument, etc.), I might find analytic asymptotic forms to test limiting cases of more general numerical code.
You probably have different applications for which different tests can be devised.
Ronald
You need to write a protocol for validation that conforms to the standards that apply to the application your code will have. Generally a test is needed, but you have to decide how many of what type, and how they will be done and reported.
Validation usually means that you can decrease the number of in process tests, but still get an acceptable result by testing the inputs and out puts. But in creating the validation the in process tests are done to show repeatability and conformance to requirements.
May be useful following stages of modeling:
1 construction of a mathematical model
2 development of a numerical method for implementing a model on a computer
3 verification of model adequacy (verification and validation):
3.1 verification of the developed numerical method
3.2 validation of the mathematical model by comparing the results of computational experiments with the model with the experimental data!
Following links also may be interesting... :)
Article Optimization of Highly-Structured Mechanical Systems with Ab...
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Presentation 2_2_Lecture_Methods of constructing mathematical models
Presentation 1_1_Lecture_Mathematical models_Математические модели
TRy to compare in analytical domain and also try to match with previously existing literature and experimental results; in case you are unable to perform experiment. In theory you have flexibility to go to that situations where experimental data is not available or possible to generate.
1. checking the theory
2. checking the algorithm
are two different concepts.
1. Theory:
For checking the theory you have to find some published results or use some geometries with available closed form analytical solution. Checking the theory should be done with respect to various loading conditions. A mistake in the shear term of a constitutive theory may not effect the results in uniaxial tension. So, the validation should be done with respect to all deformation modes of the particular problem.
2. Algorithm
When you check the algorithm;
i. convergence rate
ii. convergence to the correct analytical result is important.
Some algorithms may exhibit strong convergence in homogeneous problems and fail in inhomogeneous ones. Some algorithms may fail under unloading branch of a cyclic test. So, the answer to your problem will depend on the type of the problem. Your algorithm may exhibit very good convergence to a numerical error threshold and not converging to the analytical result exhibiting locking phenomena.
I hope this this helps.
Good luck!
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