Documents published in Scipedia

• Vectorised spectral/hp element matrix-free operator for anisotropic heat transport in tokamak edge plasma

  B. Liu, C. Cantwell, D. Moxey, M. Green, S. Sherwin

  eccomas2022.

  
  

  Abstract

  A highly efficient matrix-free Helmholtz operator with single-instruction multipledata (SIMD) vectorisation is implemented in Nektar++ [1] and applied to the simulation of anisotropic heat transport in tokamak edge plasma. A tokamak is currently the leading candidate for a practical fusion reactor using the magnetic confinement approach to produce electricity through controlled thermonuclear fusion. Predicting the transport of heat in magnetized plasma is important to designing a safe tokamak design. Due to the ionized nature of plasma, the heat conduction of the magnetized plasma is highly anisotropic along the magnetic field lines. In this study, a variational form is proposed to simulate the anisotropic heat transport in magnetized plasma and the details of its mathematical derivation and implementation are presented. To accurately approximate the thermal load of plasma deposition on the wall of tokamak chamber, highly scalable and efficient algorithms are crucial. To achieve this, a matrix-free Helmholtz operator is implemented in the Nektar++ framework, utilising sum-factorisation to reduce the operation count and increase arithmetic intensity, and leveraging SIMD vectorisation to accelerate the computation on modern hardware. The performance of the implementation is assessed by measuring throughput and speed-up of the operators using deformed and regular quadrilateral and triangular elements.

  Abstract
  A highly efficient matrix-free Helmholtz operator with single-instruction multipledata (SIMD) vectorisation is implemented in Nektar++ [1] and applied to the simulation of [...]

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• The neural network multigrid solver for the Navier-Stokes equations and its application to 3D simulation

  N. Margenberg, C. Lessig, T. Richter

  eccomas2022.

  
  

  Abstract

  We investigate scaling and efficiency of the deep neural network multigrid method (DNN-MG), a novel neural network-based technique for the simulation of the Navier-Stokes equations that combines an adaptive geometric multigrid solver with a recurrent neural network with memory. The neural network replaces in DNN-MG one or multiple finest multigrid layers and provides a correction for the classical solve in the next time step. This leads to little degradation in the solution quality while substantially reducing the overall computational costs. At the same time, the use of the multigrid solver at the coarse scales allows for a compact network that is easy to train, generalizes well, and allows for the incorporation of physical constraints. In this work, we investigate how the network size affects training and solution quality and the overall runtime of the computations.

  Abstract
  We investigate scaling and efficiency of the deep neural network multigrid method (DNN-MG), a novel neural network-based technique for the simulation of the Navier-Stokes [...]

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• Evaluation of the performance portability layer of different linear solver packages with ALIEN, an open generic and extensible linear algebra framework

  J. GRATIEN, C. Chevalier, T. Guignon, X. Tunc, P. Have, S. De Chaisemartin

  eccomas2022.

  
  

  Abstract

  Applications to solve large and complex partial derivative equation systems often rely nowadays on frameworks like Arcane, Dune, Feel++. Linear solver packages like PETSc or Trilinos are used to manage linear systems and provide access to a wide range of algorithms. With the evolution of High-Performance Computing, the variety of the hardware features available in new architectures has considerably increased. ARM processors, AMD, Intel and Nvidia GP-GPUs, TPU and FPGA devices are now common. To handle the induced complexity, different strategies are adopted in each linear solver framework. One of them consists in introducing a new layer that provides abstractions to manage the performance portability and to enable several parallel programming models. In this paper, we evaluate the performance of linear solver packages that rely on tools like SYCL [16], Kokkos [8] or HARTS [11] to handle runtime systems like OpenMP, TBB, CUDA,. . . . A simulator to solve advection-diffusion problems has been developed with ALIEN, a C++ framework that provides a high level and unified API to handle large distributed matrices and vectors. We have benchmarked different solver algorithms, and have evaluated the efficiency of their implementations, and their capability to perform on different architectures, for instance, large number of cores, GP-GPU accelerators, or processors with large SIMD instructions.

  Abstract
  Applications to solve large and complex partial derivative equation systems often rely nowadays on frameworks like Arcane, Dune, Feel++. Linear solver packages like PETSc [...]

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• A Factorization Algorithm for Sparse Matrix with Mixed Precision Arithmetic

  A. Suzuki

  eccomas2022.

  
  

  Abstract

  A new hybrid algorithm for LDU -factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. The last Schur complement will be generated by iterative solver for multiple right-hand sides using block GCR method with the factorization in lower precision as a preconditioner, which achieves mixed precision arithmetic, and then the Schur complement will be factorized in higher precision. In this algorithm, essential procedure is decomposition of the matrix into a union of moderate and hard parts, which is realized by LDU -factorization in lower precision with symmetric pivoting and threshold postponing technique.

  Abstract
  A new hybrid algorithm for LDU -factorization for large sparse matrix combining iterative solver, which can keep the same accuracy as the classical factorization, is proposed. [...]

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• Very fast FEM Poisson solvers on lower precision accelerator hardware

  D. Ruda, S. Turek, D. Ribbrock, P. Zajac

  eccomas2022.

  
  

  Abstract

  Graphics cards that are equipped with Tensor Core units designed for AI applications, for example the NVIDIA Ampere A100, promise very high peak rates concerning their computing power (156 TFLOP/s in single and 312 TFLOP/s in half precision in the case of the A100). This is only achieved when performing arithmetically intensive operations such as dense matrix multiplications in the aforementioned lower precision, which is an obstacle when trying to use this hardware for solving linear systems arising from PDEs discretized with the finite element method. In previous works, we delivered a proof of concept that the predecessor of the A100, the V100 and its Tensor Cores, can be exploited to a great extent when solving Poisson's equation on the unit square if a hardware-oriented direct solver based on prehandling via hierarchical finite elements and a Schur complement approach is used. In this work, using numerical results on an A100 graphics card, we show that the method also achieves a very high performance if Poisson's equation, which is discretized by linear finite elements, is solved on a more complex domain corresponding to a flow around a square configuration.

  Abstract
  Graphics cards that are equipped with Tensor Core units designed for AI applications, for example the NVIDIA Ampere A100, promise very high peak rates concerning their computing [...]

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• Material point method for large deformation seismic response analysis

  M. Kohler, A. Stöcklin, A. Puzrin

  eccomas2022.

  
  

  Abstract

  Landslides triggered by earthquakes are one of the major seismic hazards and can cause large damages and fatalities. The material point method (MPM) has become a popular technique to model such large mass movements. A limitation of existing MPM implementations is the lack of appropriate boundary conditions to perform seismic response analysis of slopes. To bridge this gap, an extension to the basic MPM framework is presented for simulating the seismic triggering and subsequent collapse of slopes within a single analysis step. The concepts of a compliant base boundary and free-field columns are applied within the MPM framework enabling the direct application of input ground motions and accounting for the absorption of outgoing waves.

  Abstract
  Landslides triggered by earthquakes are one of the major seismic hazards and can cause large damages and fatalities. The material point method (MPM) has become a popular technique [...]

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• Penalized direct-dorcing method and power-law-based wall model for immersed-boundary numerical simulations of obstacles in turbulent flow

  I. Hamadache, M. Belliard, P. Sagaut

  eccomas2022.

  
  

  Abstract

  In this paper, academic and industrial test cases have been conducted in order to validate the approach of using a Penalized Direct Forcing method coupled with an immersed turbulent wall model. Good results are obtained compared to a body fitted mesh with the Werner & Wengle wall model. In a shortcoming second step, we can project the coupling between the immersed wall law and a K-epsilon model, as well as obstacle shape optimization during the flow computation.

  Abstract
  In this paper, academic and industrial test cases have been conducted in order to validate the approach of using a Penalized Direct Forcing method coupled with an immersed [...]

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• A comparison between IBM with feedback forcing and a volume penalization method for compressible flows

  L. Ménez, E. Goncalves, P. Parnaudeau, D. Colombet

  eccomas2022.

  
  

  Abstract

  The aim of this work is to model compressible flows involving shock waves past a solid obstacle using a non-conformal mesh. An Immersed Boundary Method (IBM) with feedback forcing and a volume penalization method are considered and compared. Both methods are validated on various test-cases. Accuracy and computational cost are discussed.

  Abstract
  The aim of this work is to model compressible flows involving shock waves past a solid obstacle using a non-conformal mesh. An Immersed Boundary Method (IBM) with feedback [...]

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• Simulation of the flow-acoustic-structural interaction in flow ducts using a partitioned approach in the time domain

  J. Kersschot, H. Denayer, W. De Roeck, W. Desmet

  eccomas2022.

  
  

  Abstract

  Duct systems confining a subsonic air flow, such as ventilation ducts, often have a lightweight design. These lightweight constructions are easily excited by unsteady pressure fluctuations in the flow, causing structural vibrations and noise emissions. Designing effective solutions for this flow-acousticstructural problem requires a better understanding of the multi-physical interactions and efficient prediction tools. In this work, due to the confined configuration, the vibro-acoustic interaction is a strong two-way interaction and is modeled by coupling a flow-acoustic solver with a structural solver. The kinematic and dynamic continuity at the interface is ensured in this partitioned approach by a data exchange during runtime between the solvers. The data exchange is managed by the open-source coupling library preCICE [1]. The analysis of the flow-acoustic-structural interaction in a flexible flow duct with rectangular cross section was given in [2]. In this paper, the error resulting from the pressure mapping between both solvers is analyzed and an improved force mapping strategy is adopted.

  Abstract
  Duct systems confining a subsonic air flow, such as ventilation ducts, often have a lightweight design. These lightweight constructions are easily excited by unsteady pressure [...]

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• Adaptive and flexible macro-micro coupling software

  I. Desai, B. Uekermann, C. Bringedal

  eccomas2022.

  
  

  Abstract

  Many multiscale simulation problems require a many-to-one coupling between different scales. For such coupled problems, researchers oftentimes focus on the coupling methodology, but largely ignore software engineering and high-performance computing aspects. This can lead to inefficient use of hardware resources, on the one hand, but also inefficient use of human resources as solutions to typical technical coupling problems are constantly reinvented. This work proposes a flexible and application-agnostic software framework to couple independent simulation codes in a many-to-one fashion. To this end, we introduce a prototype of a new lightweight software component called Micro Manager, which allows us to reuse the coupling library preCICE for two-scale coupled problems. We demonstrate the applicability of the framework by a two-scale coupled heat conduction problem.

  Abstract
  Many multiscale simulation problems require a many-to-one coupling between different scales. For such coupled problems, researchers oftentimes focus on the coupling methodology, [...]

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