Documents published in Scipedia

• Implicit Schur complement iterative modal solvers for multiphysics model order reduction

  G. Buron, F. Thouverez, L. Jézéquel, A. Beley, F. Thévenon

  coupled2023.

  
  

  Abstract

  In this work, we propose iterative modal solvers to generate multiphysics finite element reduced order models. We consider the strongly coupled problems defined through differential-algebraic equations with sparse discrete operators. Piezoelectric models are common examples of such problems. The approach we propose is based on the Model Order Reduction (MOR) after Implicit Schur method [1] which is used for the Krylov subspace reduction of piezoelectric devices. While their work uses the knowledge of the loading applied to the model to generate a Krylov subspace reduction basis, we propose to build a reduction basis with a priori unknown loading by modal synthesis. The basis is built from the eigenvectors of the problem after the static condensation by Schur complement of one of the physics. Typically, the Schur complement matrix is computed explicitly and it leads to dense operators [2] which limit the problem scales that can be studied due to large memory requirements and costly computations for the eigensolver used afterward. For Krylov-based eigensolvers, the most computationally difficult step is to obtain a basis spanning the eigenspace of the problem on the considered eigenvalue range. By generalizing the MOR after Implicit Schur method, this basis can be constructed by an iterative procedure using the original sparse operators instead of the dense condensed operators. The original model may be significantly larger compared to the condensed model for typical cases. However, keeping the sparsity is a critical computational advantage for the considered problems. This method is minimally intrusive for the eigensolvers that only require the implementation of a matrix-vector product. Comparing this implicit Schur complement approach to the explicit Schur complement approach shows large computational cost reductions. It also underlines the problem scale limitations of the explicit approach even on high performance computing hardware.

  Abstract
  In this work, we propose iterative modal solvers to generate multiphysics finite element reduced order models. We consider the strongly coupled problems defined through differential-algebraic [...]

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• Time adaptive Waveform-Relaxation methods for Fluid Structure Interaction

  P. Birken, N. Kortasky

  coupled2023.

  
  

  Abstract

  We consider waveform iterations for dynamic coupled problems with respect to the role of time window length. We review existing theoretical results about the error of waveform iterations and the role of the time window length. Furthermore, we present numerical results for waveform iterations with both time adaptive sub solvers and with fixed time steps. This way, we are able to give a recommendation on the choice of the time window. The use of time windows can lead to an increase in efficiency. For fixed time grids, we can reliably achieve a small performance increase. For time adaptive solvers, more research is needed.

  Abstract
  We consider waveform iterations for dynamic coupled problems with respect to the role of time window length. We review existing theoretical results about the error of waveform [...]

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• The effect of the number of subproblem iterations in partitioned fluid-structure interaction simulation

  N. Delaissé, T. Spenke, N. Hosters, J. Degroote

  coupled2023.

  
  

  Abstract

  In a partitioned fluid-structure interaction simulation separate flow and structure solvers, each with their own spatial domain, are coupled by exchanging data on the common interface. Its computational cost is dominated by the execution of these solvers, and the cost associated with the coupling algorithm and communication are often deemed negligible. From this point of view, the computational cost is in literature typically expressed by the number of required coupling iterations per time step or equivalently the number of solver executions. However, this reasoning implicitly assumes a constant solver cost and ignores the varying number of internal subproblem iterations, i.e., solver iterations in the nonlinear solvers. This work addresses this shortcoming and shows that the computational cost of a partitioned fluid-structure interaction simulation is significantly impacted by the number of subproblem iterations performed in each solver call. Specifically, it is demonstrated that performing subproblem iterations until the solver is fully converged in each call does typically minimize the number of coupling iterations, but does not lead to minimal computational time. Instead, under the assumption of constant subproblem iteration cost, the optimum is found by minimizing a weighted sum of both coupling and subproblem iterations. The weighting factors are determined by the problem itself as well as the computer architecture.

  Abstract
  In a partitioned fluid-structure interaction simulation separate flow and structure solvers, each with their own spatial domain, are coupled by exchanging data on the common [...]

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• Introducing a cloud-based framework for creating, visualising, testing and automating complex simulation workflows

  O. Stodieck

  coupled2023.

  
  

  Abstract

  Engineers increasingly need tools that help them automate complex simulation workflows. Besides performance, robustness and usability requirements, tools should also be easily accessible. To fulfil these requirements, Dapta Ltd is developing a cloud-based framework, which is designed to be an all-in-one solution to create, visualise, test and automate simulation workflows. Here we demonstrate the use of the dapta platform with open-source software libraries, focusing on an FSI multiphysics example.

  Abstract
  Engineers increasingly need tools that help them automate complex simulation workflows. Besides performance, robustness and usability requirements, tools should also be easily [...]

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• Multistep interface coupling for high-order adaptive black-box multiphysics simulations

  L. François, M. Massot

  coupled2023.

  
  

  Abstract

  Many multiphysics problem can be described by the coupling of several models through physical surfaces. Relying on existing model-specific solvers is very desirable, however they must be coupled in a way that ensures an accurate and stable coupled simulation. In this contribution, we present a multistep coupling scheme which relies on the history of the exchanged quantities to enable a high-order accurate coupling with time adaptation. Explicit and implicit variants are discussed in details. Numerical experiments conducted with an opensource demonstrator on a conjugate heat transfer problem show that high-order convergence is attained, and that stability is favourable compared to other classical approaches.

  Abstract
  Many multiphysics problem can be described by the coupling of several models through physical surfaces. Relying on existing model-specific solvers is very desirable, however [...]

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• Partitioned MPM-FEM Coupling Approach for Advanced Numerical Simulation of Mass-Movement Hazards Impacting Flexible Protective Structures

  V. Singer, A. Laresse, R. Wüchner, K. Bletzinger

  coupled2023.

  
  

  Abstract

  The intensity and frequency of natural hazards such as landslides, debris flow, and mud flows have increased significantly over the last years due to climate change and global warming. These catastrophic events are responsible for numerous destructions of infrastructures and landscapes and often even claim human lives. Therefore, in addition to the prediction, the design and installation of protective structures are of tremendous importance. In recent decades, highly flexible protective structures have been favored due to their enormous energy absorption capacity while adapting well to the environment. However, dimensioning such protective structures is a very complex task requiring advanced numerical simulation techniques. To capture the behavior of such natural hazards on the one hand and the highly flexible protection structures, including complex elements such as sliding cables or brakes on the other hand, a partitioned coupling approach is proposed in this work. This way, the most appropriate solvers, treated as black-box solvers, can be selected for each physics involved while the interaction is shifted to the shared interface.

  Abstract
  The intensity and frequency of natural hazards such as landslides, debris flow, and mud flows have increased significantly over the last years due to climate change and global [...]

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• Partitioned MPM-FEM Coupling Approach for Advanced Numerical Simulation of Mass-Movement Hazards Impacting Flexible Protective Structures

  V. Singer, A. Laresse, A. Börst, R. Wüchner, K. Bletzinger

  coupled2023.

  
  

  Abstract

  The intensity and frequency of natural hazards such as landslides, debris flow, and mud flows have increased significantly over the last years due to climate change and global warming. These catastrophic events are responsible for numerous destructions of infrastructures and landscapes and often even claim human lives. Therefore, in addition to the prediction, the design and installation of protective structures are of tremendous importance. In recent decades, highly flexible protective structures have been favored due to their enormous energy absorption capacity while adapting well to the environment. However, dimensioning such protective structures is a very complex task requiring advanced numerical simulation techniques. To capture the behavior of such natural hazards on the one hand and the highly flexible protection structures, including complex elements such as sliding cables or brakes on the other hand, a partitioned coupling approach is proposed in this work. This way, the most appropriate solvers, treated as black-box solvers, can be selected for each physics involved while the interaction is shifted to the shared interface.

  Abstract
  The intensity and frequency of natural hazards such as landslides, debris flow, and mud flows have increased significantly over the last years due to climate change and global [...]

  • 0
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• A certified wavelet-based physics-informed neural network for the solution of parameterized partial differential equations

  L. Ernst, K. Urban

  coupled2023.

  
  

  Abstract

  Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error, which is particularly relevant for model reduction of Parameterized PDEs (PPDEs). To this end, we suggest to use a weighted sum of expansion coefficients of the residual in terms of an adaptive wavelet expansion both for the loss function and an error bound. This approach is shown here for elliptic PPDEs using both the standard variational and an optimally stable ultra-weak formulation. Numerical examples show a very good quantitative effectivity of the wavelet-based error bound.

  Abstract
  Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct [...]

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• Multiphysical Modeling of Soft Tissue-Stent Interaction

  S. Reese, K. Manjunatha, J. Shi, M. Sesa

  coupled2023.

  
  

  Abstract

  The prevalence of in-stent restenosis after percutaneous coronary intervention necessitates the development of computational tools to derive pathophysiological inferences and finetune interventional procedures patient-specifically. In this context, a multiphysics framework is presented herein that captures the chemo-mechano-biological interaction involved. Strategies that could potentially accelerate the computations as well as add versatility to them are shortly discussed. We hence take a minute step towards enabling computer-assisted clinical practices.

  Abstract
  The prevalence of in-stent restenosis after percutaneous coronary intervention necessitates the development of computational tools to derive pathophysiological inferences [...]

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• On the 2D-1D Coupling in Numerical Simulations of Simplified Air Flow Model in Human Airways

  coupled2023.

  
  

  Abstract

  This paper presents selected results regarding the implementation, validation and testing of a simple 2D-1D coupled model designed to capture some essential features of the oscillatory air flow in human respiratory system. The model relies on a 2D flow model solved by a simple finite-difference scheme in the immersed boundary setting. The incompressible fluid flow from this model is coupled to a simplified 1D fluid-structure-interaction model simulating the flow in a tube with elastic walls. Some first results obtained using the coupled 2D-1D model in an oscillating (Womersley-like) type of flow are presented and discussed in detail. The influence of model parameters is explored for a range of physically relevant settings.

  Abstract
  This paper presents selected results regarding the implementation, validation and testing of a simple 2D-1D coupled model designed to capture some essential features of the [...]

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