René Milk

pyMOR -- Generic Algorithms and Interfaces for Model Order Reduction

Reduced basis methods are projection-based model order reduction techniques for reducing the computational complexity of solving parametrized partial differential equation problems. In this work we discuss the design of pyMOR, a freely available software library of model order reduction algorithms, in particular reduced basis methods, implemented with the Python programming language. As its main design feature, all reduction algorithms in pyMOR are implemented generically via operations on well-defined vector array, operator and discretization interface classes. This allows for an easy integration with existing open-source high-performance partial differential equation solvers without adding any model reduction specific code to these solvers. Besides an in-depth discussion of pyMORs design philosophy and architecture, we present several benchmark results and numerical examples showing the feasibility of our approach.

Hardware-Based Efficiency Advances in the EXA-DUNE Project

We present advances concerning efficient finite element assembly and linear solvers on current and upcoming HPC architectures obtained in the frame of the Exa-Dune project, part of the DFG priority program 1648 Software for Exascale Computing (SPPEXA). In this project, we aim at the development of both flexible and efficient hardware-aware software components for the solution of PDEs based on the DUNE platform and the FEAST library. In this contribution, we focus on node-level performance and accelerator integration, which will complement the proven MPI-level scalability of the framework. The higher-level aspects of the Exa-Dune project, in particular multiscale methods and uncertainty quantification, are detailed in the companion paper (Bastian et al., Advances concerning multiscale methods and uncertainty quantification in Exa-Dune. In: Proceedings of the SPPEXA Symposium, 2016).

Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo

Uncertainty quantification (UQ) for porous media flow is of great importance for many societal, environmental and industrial problems. An obstacle for progress in this area is the extreme computational effort needed for solving realistic problems. It is expected that exa-scale computers will open the door for a significant progress in this area. We demonstrate how new features of the Distributed and Unified Numerics Environment DUNE [1] address these challenges. In the frame of the DFG funded project EXA-DUNE the software has been extended by multiscale finite element methods (MsFEM) and by a parallel framework for the multilevel Monte Carlo (MLMC) approach. This is a general concept for computing expected values of simulation results depending on random fields, e.g. the permeability of porous media. It belongs to the class of variance reduction methods and overcomes the slow convergence of classical Monte Carlo by combining cheap/inexact and expensive/accurate solutions in an optimal ratio.

Extending DUNE: The dune-xt modules

Abstract: We present our effort to extend and complement the core modules of the Dis- tributed and Unified Numerics Environment DUNE (http://dune-project.org) by a well tested and structured collection of utilities and concepts. We describe key elements of our four modules dune-xt-common, dune-xt-grid, dune-xt-la and dune-xt-functions, which aim add further enabling the programming of generic algorithms within DUNE as well as adding an extra layer of usability and convenience.

Advances Concerning Multiscale Methods and Uncertainty Quantification in EXA-DUNE

In this contribution we present advances concerning efficient parallel multiscale methods and uncertainty quantification that have been obtained in the frame of the DFG priority program 1648 Software for Exascale Computing (SPPEXA) within the funded project Exa-Dune. This project aims at the development of flexible but nevertheless hardware-specific software components and scalable high-level algorithms for the solution of partial differential equations based on the DUNE platform. While the development of hardware-based concepts and software components is detailed in the companion paper (Bastian et al., Hardware-based efficiency advances in the Exa-Dune project. In: Proceedings of the SPPEXA Symposium 2016, Munich, 25–27 Jan 2016), we focus here on the development of scalable multiscale methods in the context of uncertainty quantification. Such problems add additional layers of coarse grained parallelism, as the underlying problems require the solution of many local or global partial differential equations in parallel that are only weakly coupled.