NACHOS Research team
Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
The research activities of the project-team are concerned with the formulation, analysis and evaluation of numerical methods and high performance resolution algorithms for the computer simulation of evolution problems in complex domains and heterogeneous media. The team concentrates its efforts on the study of PDE models of electromagnetics and elastodynamics.
The physical and geometrical characteristics of the applications of interest to the project-team research activities motivate the design of accurate, efficient and robust discretization methods for the involved systems of PDEs. We concentrate on high-order (polynomial interpolation), non-conforming (h-, p- and hp-adaptivity) discontinuous finite element methods, formulated on triangulations (2D case) or tetrahedrizations (3D case) of the underlying computational domain. Furthermore, in order to allow for the simulation of realistic physical problems, we investigate the numerical treatment of complex material models in the framework of these discretization methods.
Explicit time integration schemes are subjected to stability conditions that become very restrictive when the underlying mesh is locally refined, especially in 3D. To overcome this problem, we study locally implicit schemes (hybrid explicit/implicit schemes) which possess advantageous stability and accuracy properties.
The design of high performance resolution algorithms is an important aspect of the research activities of the project-team. In this respect, we study domain decomposition resolution algorithms, more precisely Schwarz algorithms based on optimized interface conditions adapted to the underlying PDE systems.
In view of the implementation of the resulting methodologies and the realization of large-scale numerical simulations, we study parallelization strategies that best exploit the characteristics of modern high performance computing architectures, in particular hybrid shared memory/distributed memory multi-processor/multi-core platforms.
International and industrial relations
- LNCC (National Laboratory for Scientific Computing), Petropolis, Brazil
- UESTC (University of Electronic Science and Technology of China), Chengdu, China
Keywords: Computational electromagnetics
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- ECUADOR - Program transformations for scientific computing
- ELAN - modELing the Appearance of Nonlinear phenomena
- GAMMA - Adaptive Mesh Generation and Advanced numerical Methods
- MATHERIALS - MATHematics for MatERIALS
- MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS
- MINGUS - MultI-scale Numerical Geometric Schemes
- MOKAPLAN - Advances in Numerical Calculus of Variations
- RAPSODI - Reliable numerical approximations of dissipative systems.
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