1,078 research outputs found
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Schnelle Löser für partielle Differentialgleichungen
The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch(Leipzig), Gabriel Wittum (Heidelberg) was held May 22nd - May 28th, 2005. This meeting was well attended by 47 participants with broad geographic representation from 9 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds
A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing
This work introduces an innovative parallel, fully-distributed finite element
framework for growing geometries and its application to metal additive
manufacturing. It is well-known that virtual part design and qualification in
additive manufacturing requires highly-accurate multiscale and multiphysics
analyses. Only high performance computing tools are able to handle such
complexity in time frames compatible with time-to-market. However, efficiency,
without loss of accuracy, has rarely held the centre stage in the numerical
community. Here, in contrast, the framework is designed to adequately exploit
the resources of high-end distributed-memory machines. It is grounded on three
building blocks: (1) Hierarchical adaptive mesh refinement with octree-based
meshes; (2) a parallel strategy to model the growth of the geometry; (3)
state-of-the-art parallel iterative linear solvers. Computational experiments
consider the heat transfer analysis at the part scale of the printing process
by powder-bed technologies. After verification against a 3D benchmark, a
strong-scaling analysis assesses performance and identifies major sources of
parallel overhead. A third numerical example examines the efficiency and
robustness of (2) in a curved 3D shape. Unprecedented parallelism and
scalability were achieved in this work. Hence, this framework contributes to
take on higher complexity and/or accuracy, not only of part-scale simulations
of metal or polymer additive manufacturing, but also in welding, sedimentation,
atherosclerosis, or any other physical problem where the physical domain of
interest grows in time
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Preparing sparse solvers for exascale computing.
Sparse solvers provide essential functionality for a wide variety of scientific applications. Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi-physics and multi-scale simulations, especially as we target exascale platforms. This paper describes the challenges, strategies and progress of the US Department of Energy Exascale Computing project towards providing sparse solvers for exascale computing platforms. We address the demands of systems with thousands of high-performance node devices where exposing concurrency, hiding latency and creating alternative algorithms become essential. The efforts described here are works in progress, highlighting current success and upcoming challenges. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'
A Unified Framework for Parallel Anisotropic Mesh Adaptation
Finite-element methods are a critical component of the design and analysis procedures of many (bio-)engineering applications. Mesh adaptation is one of the most crucial components since it discretizes the physics of the application at a relatively low cost to the solver. Highly scalable parallel mesh adaptation methods for High-Performance Computing (HPC) are essential to meet the ever-growing demand for higher fidelity simulations. Moreover, the continuous growth of the complexity of the HPC systems requires a systematic approach to exploit their full potential. Anisotropic mesh adaptation captures features of the solution at multiple scales while, minimizing the required number of elements. However, it also introduces new challenges on top of mesh generation. Also, the increased complexity of the targeted cases requires departing from traditional surface-constrained approaches to utilizing CAD (Computer-Aided Design) kernels. Alongside the functionality requirements, is the need of taking advantage of the ubiquitous multi-core machines. More importantly, the parallel implementation needs to handle the ever-increasing complexity of the mesh adaptation code.
In this work, we develop a parallel mesh adaptation method that utilizes a metric-based approach for generating anisotropic meshes. Moreover, we enhance our method by interfacing with a CAD kernel, thus enabling its use on complex geometries. We evaluate our method both with fixed-resolution benchmarks and within a simulation pipeline, where the resolution of the discretization increases incrementally. With the Telescopic Approach for scalable mesh generation as a guide, we propose a parallel method at the node (multi-core) for mesh adaptation that is expected to scale up efficiently to the upcoming exascale machines. To facilitate an effective implementation, we introduce an abstract layer between the application and the runtime system that enables the use of task-based parallelism for concurrent mesh operations. Our evaluation indicates results comparable to state-of-the-art methods for fixed-resolution meshes both in terms of performance and quality. The integration with an adaptive pipeline offers promising results for the capability of the proposed method to function as part of an adaptive simulation. Moreover, our abstract tasking layer allows the separation of different aspects of the implementation without any impact on the functionality of the method
Task-based adaptive multiresolution for time-space multi-scale reaction-diffusion systems on multi-core architectures
A new solver featuring time-space adaptation and error control has been
recently introduced to tackle the numerical solution of stiff
reaction-diffusion systems. Based on operator splitting, finite volume adaptive
multiresolution and high order time integrators with specific stability
properties for each operator, this strategy yields high computational
efficiency for large multidimensional computations on standard architectures
such as powerful workstations. However, the data structure of the original
implementation, based on trees of pointers, provides limited opportunities for
efficiency enhancements, while posing serious challenges in terms of parallel
programming and load balancing. The present contribution proposes a new
implementation of the whole set of numerical methods including Radau5 and
ROCK4, relying on a fully different data structure together with the use of a
specific library, TBB, for shared-memory, task-based parallelism with
work-stealing. The performance of our implementation is assessed in a series of
test-cases of increasing difficulty in two and three dimensions on multi-core
and many-core architectures, demonstrating high scalability
The Peano software---parallel, automaton-based, dynamically adaptive grid traversals
We discuss the design decisions, design alternatives, and rationale behind the third generation of Peano, a framework for dynamically adaptive Cartesian meshes derived from spacetrees. Peano ties the mesh traversal to the mesh storage and supports only one element-wise traversal order resulting from space-filling curves. The user is not free to choose a traversal order herself. The traversal can exploit regular grid subregions and shared memory as well as distributed memory systems with almost no modifications to a serial application code. We formalize the software design by means of two interacting automata—one automaton for the multiscale grid traversal and one for the application-specific algorithmic steps. This yields a callback-based programming paradigm. We further sketch the supported application types and the two data storage schemes realized before we detail high-performance computing aspects and lessons learned. Special emphasis is put on observations regarding the used programming idioms and algorithmic concepts. This transforms our report from a “one way to implement things” code description into a generic discussion and summary of some alternatives, rationale, and design decisions to be made for any tree-based adaptive mesh refinement software
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