
Nils-Arne DreierUniversity of Münster | WWU · Institute of Computational and Applied Mathematics
Nils-Arne Dreier
Master of Science
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11
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Introduction
Publications
Publications (11)
The orthogonalization process is an essential building block in Krylov space methods, which takes up a large portion of the computational time. Commonly used methods, like the Gram-Schmidt method, consider the projection and normalization separately and store the orthogonal base explicitly. We consider the problem of orthogonalization and normaliza...
Krylov subspace methods are an essential building block in numerical simulation software. The efficient utilization of modern hardware is a challenging problem in the development of these methods. In this work, we develop Krylov subspace methods to solve linear systems with multiple right-hand sides, tailored to modern hardware in high-performance...
It is expected that with the appearance of exascale supercomputers the mean time between failure in supercomputers will decrease. Classical checkpoint-restart approaches are too expensive at that scale. Local-failure local-recovery (LFLR) strategies are an option that promises to leverage the costs, but actually implementing it into any sufficientl...
Block Krylov methods have recently gained a lot of attraction. Due to their increased arithmetic intensity they offer a promising way to improve performance on modern hardware. Recently Frommer et al. (Electron Trans Numer Anal 47:100–126, 2017). presented a block Krylov framework that combines the advantages of block Krylov methods and data parall...
This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007 and the main papers describing that state Bastian etal. (2008a, 2008b). This discussion is accompanied with a de...
In the Exa-Dune project we have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively parallel architecture. In order to cope with the increased probability of hardware failures, one aim of the project...
Block Krylov methods have recently gained a lot of attraction. Due to their increased arithmetic intensity they offer a promising way to improve performance on modern hardware. Recently Frommer et al. presented a block Krylov framework that combines the advantages of block Krylov methods and data parallel methods. We review this framework and apply...
In the Exa-Dune project we have developed, implemented and optimised numerical algorithms and software for the scalable solution of partial differential equations (PDEs) on future exascale systems exhibiting a heterogeneous massively parallel architecture. In order to cope with the increased probability of hardware failures, one aim of the project...
This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007 and the main papers describing that state [1, 2]. This discussion is accompanied with a description of various a...
We propose a new particle based method for simulating incompressible Navier‐Stokes flows. It is based on a reinterpretation of the optimal transportation meshfree method within the context of Galerkin discretization. This enables us to introduce the incompressibility constraint into the formulation. Furthermore, we present convergence test and illu...