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Banner Priority Programme DFG 1648



Poster NIC Symposium 2016

Poster I: Materials Chain 2016

Poster II: Materials Chain 2016


The macroscopic behavior of advanced high strength steel is governed by the complex interactions of the individual constituents on the microscale. Simulations of challenging multiphase steel structural problems as the deep-drawing of automotive parts require accurate predictive material models incorporating the material's microstructure evolution during the thermomechanical process.

Radical Scale Briding FE² - Framework

The FE²-method, cf. e.g. [1], is a direct multiscale method and provides a suitable numerical tool for radical scale bridging:


However the computational requirements are still enormous in 3D and necessitate efficient algorithms at the exascale.

Steel RVE and Co.

Mechanical Modeling at the Microscale

At the microscale Representative Volume Elements (RVEs), see [2], are considered and the material behavior of the individual constituents is described by a finite plasticity model. In order to incorporate initial hardening distributions phase transformations of the original austenitic inclusions to martensite need to be modeled accurately and thus a crystallographically motivated model is planned to be developed in the line of [3].

To derive at a suitable microscopic model an approach for the homogenization of different lattice orientations has to be developed.


describes the stress state in the inclusion. Phase transformations require the incorporation of thermo-mechanics into the FE²-scheme and the derivation of associated consistent tangent moduli.

Parallel Application Software

Parallelization on several levels will be used to accomplish the scale bridging. The level with the highest granularity is the parallel solution of the many highly nonlinear RVE problems. The remaining orders of magnitude will be bridged by ultra-scalable solvers. The legacy application software FEAP will be used for the FE technology. A strong collaboration of all PIs is essential to create the correct infrastructure for all following steps. New ultra-scalable solvers for nonlinear problems will profit from an earlier DFG project on parallel nonlinear structural mechanics. The solvers will be based on FETI (Finite Element Tearing and Interconnecting) approaches thus reducing communication compared to other DD methods.

Solvers -- Combine Domain Decomposition (DD) and Multigrid (MG) Methods

scaling example irFETI-DP


  • (ir)FETI-DP-type DD methods

    have scaled to 10⁴ - 10⁵ cores [4].

  • Algebraic MG DD methods

    have scaled to 10⁴ - 10⁵ cores [5].


Recent iFETI-DP algorithms [4] are methods to solve the linear saddle point problem

FEI-DP saddle point problem

with a preconditioner

FEI-DP preconditioner

We will construct new, ultra-scalable Algebraic MG preconditioners as building blocks instead of direct solvers. Performance modeling and engineering will guide the development in a systematic process - years before exascale computers become available. Fault resilient AMG strategies will be applied.

Solvers - Nonlinear, nonoverlapping DD

Increased local work will reduce communication and the need for synchronization and thus also increase latency tolerance. Also facilitates the implementation of fault tolerance strategies. A successful overlapping nonlinear DD approach is known as ASPIN [6]. We, however, concentrate on nonoverlapping DD because of potentially smaller communication costs.

Performance Engineering, Profiling and Optimization


We implement a structured performance engineering approach. A diagnostic performance model enforces better understanding of the code and HW properties. Performance measurements will be performed using LIKWID [7]. Early insights into performance limiting factors will enable algorithmic and software redesign. Strategies for fault tolerance will be studied.




  • [1] Schröder, J. [2000], Habitilation thesis.
  • [2] Schröder, J.; Balzani, D.; Brands, D. [2010], A. App. Math.
  • [3] Turteltaub, S. & Suiker, A.S.J. [2006], Int. J. Sol. Struct.
  • [4] Klawonn, A. & Rheinbach, O. [2010], ZAMM
  • [5] Baker, A.; Falgout, R.; Kolev, T.; Meier-Yang, U., [2012], in Springer
  • [6] Cai, X.; Keyes, D.E. [2002], SIAM J. Sci.Comput.
  • [7] Treibig, J.;Hager, G.; Wellein, G. [2010], PSTI2010