Benchmarks made in the PLEIADES platform

Fuel performance codes based on the Cast3M finite element solver

Numerous performance assessments were made within the PLEIADES platform : replacing fortran implementations by their MFront counterparts led to significant improvements, from \(30\%\) to \(50\%\) of the total computational times of some fuel performance codes developed in the platform.

These improvements were mainly due to fact that the behaviour integration schemes changed from explicit Runge-Kutta schemes to implicit ones. The main benefit of MFront was to grant users an easier access to the implicit schemes.

Cyrano3 fuel performance code

Relying on the specific modelling hypotheses supported by this code, namely axisymmetrical generalised plane stress and axisymmetrical generalised plane strain, highly specialised and efficient implementations of mechanical behaviours were developed in Cyrano3 fuel performance code [see 1] for both isotropic and orthotropic materials : numerical integration boils down to solving a scalar non-linear equation in both cases and provides the consistent tangent operator.

The figure below compares the total computational times of a native implementation of a cladding behaviour to its equivalent MFront implementation: the last one appears to be competitive with the native implementation (the average computational time using the MFront implementation is sightly lower than the average computational time using the native implementation).

Benchmarks based on the Code-Aster finite element solver

Some benchmarks comparing the implementation generated through MFront to the native implementation provided by the Code-Aster finite element solver. Graphical illustrations shows that the results obtained with both implementations are indistinguishable.

Behaviour and test description	Algorithm	Total computational times (Code-Aster vs MFront)	Graphical illustration
Visco-plastic and damaging for steel [see 2, 3] - 3D Notched specimen implying large deformation	Implicit	\(17mn 43s\) vs \(7mn 58s\)
Damaging for concrete [see 4, 5], 3D beam bending	Default	\(45mn\) vs \(63mn\)
Generic Single crystal viscoplasticity [see 6, 7], 3D aggregate, 300 grains	Implicit	\(28mn\) vs \(24mn\)
FCC single crystal viscoplasticity [7] , 2D specimen with displacement boundary conditions from EBSD experiment	Ìmplicit	\(33m54s\) vs \(29m30s\)
FCC homogenized polycrystals 30 grains [7, see 9], unit testing	Runge-Kutta 4/5	\(9s67\) vs \(8s22\)
Anisotropic creep with phase transformation, 3D pipe [see 10]	Implicit	\(180s\) vs \(171s\)

Developers of the Code-Aster general purpose finite element solver, made independent extensive tests, comparing their own native implementations to the ones generated with MFront, generally using an implicit scheme in both cases. Without discussing the very details of each test performed, several general conclusions can be drawn:

• native implementations offer superior performances in the case of simple explicit behaviours (Mazars damaging behaviour [see 4]) in the case of isotropic behaviours that can be reduced to one scalar equations [see 11]. For explicit behaviours, the difference will be reduced by the development of an optimised treatment of MFront behaviours. In the second case, the difference can be explained by the fact that the Code-Aster implementations uses the Brent algorithm [see 12] which clearly outperforms the standard Newton method. The availability of this algorithm in MFront is planned.
• for more complex behaviours, MFront implementation is on par or outperforms the native implementations.

For a given behaviour, the development time was found significantly lower with MFront.

References