Domain Decomposition Research Articles

Domain Decomposition Strategy for Combining Nonlinear and Linear Reduced-Order Models

Increasingly ubiquitous reliance on expensive, high-fidelity numerical simulations has led to the emergence of reduced-order modeling as an effective method to predict high-dimensional, spatially discretized field outputs in an efficient manner. This study presents a method to construct parametric, nonintrusive reduced-order models (ROMs) by leveraging domain decomposition (DD) to enable using multiple dimension reduction (DR) techniques within different spatial subdomains of the field to construct a single predictive ROM. To enforce smoothness of solutions across subdomains, points at domain interfaces are reconstructed using the data-driven gappy proper orthogonal decomposition method. The method is assessed on three high-dimensional test cases with shocks, including one with two-dimensional turbulent flow around the RAE2822. Results show that fully nonlinear ROMs predict fields more accurately in the vicinity of discontinuous features compared to their linear counterparts, which are more accurate in regions that are far from these discontinuities. Furthermore, irrespective of the DR method, DD-based ROMs outperformed their global counterparts in all test cases. Finally, models that used a combination of DR methods simultaneously showed superior performance near shockwaves and a significant improvement in total error compared to existing approaches that employ a single DR method in all subdomains.

Reduced order modeling based inexact FETI‐DP solver for lattice structures

SummaryThis paper addresses the overwhelming computational resources needed with standard numerical approaches to simulate architected materials. Those multiscale heterogeneous lattice structures gain intensive interest in conjunction with the improvement of additive manufacturing as they offer, among many others, excellent stiffness‐to‐weight ratios. We develop here a dedicated HPC solver that benefits from the specific nature of the underlying problem in order to drastically reduce the computational costs (memory and time) for the full fine‐scale analysis of lattice structures. Our purpose is to take advantage of the natural domain decomposition into cells and, even more importantly, of the geometrical and mechanical similarities among cells. Our solver consists in a so‐called inexact FETI‐DP method where the local, cell‐wise operators and solutions are approximated with reduced order modeling techniques. Instead of considering independently every cell, we end up with only few principal local problems to solve and make use of the corresponding principal cell‐wise operators to approximate all the others. It results in a scalable algorithm that saves numerous local factorizations. Our solver is applied for the isogeometric analysis of lattices built by spline composition, which offers the opportunity to compute the reduced basis with macro‐scale data, thereby making our method also multiscale and matrix‐free. The solver is tested against various 2D and 3D analyses. It shows major gains compared to black‐box solvers; in particular, problems of several millions of degrees of freedom can be solved with a simple computer within few minutes.

OpenFuelCell2: A new computational tool for fuel cells, electrolyzers, and other electrochemical devices and processes

Fuel cells/electrolyzers are efficient and clean electrochemical devices that convert chemical energy directly into electricity and vice versa. They have attracted sustainable attention over the past decade from multiple experimental and numerical studies. However, detailed experimental investigations are typically expensive and challenging for providing a number of operating conditions and designs. Computational analysis offers an alternative approach for these studies. With the steadily increasing high-performance computing resources available, the limitations of numerical simulations have substantially decreased. This contribution details the design choice and code structure of modern electrochemical devices, which have been implemented as a versatile C++ library named openFuelCell2 within the open-source platform OpenFOAM, allowing for large-scale parallel calculations to be performed. The solver considers the major transport phenomena in a typical electrochemical device, including fluid flow, heat and mass transfer, species and charge transfer, and electrochemical reaction. This enables numerical simulations on popular electrochemical devices, such as fuel cells and electrolyzers, to be conducted. The paper also describes the domain decomposition, and parallel performance issues, as well as future applications. Program summaryProgram Title:openFuelCell2CPC Library link to program files:https://doi.org/10.17632/cvmb5xgy7h.1Developer's repository link:https://github.com/openFuelCell2/openFuelCell2Licensing provisions: GPLv3Programming language: C++Journal reference of previous version: S.B. Beale, H.-W. Choi, J.G. Pharoah, H.K. Roth, H. Jasak, D.H. Jeon, Open-source computational model of a solid oxide fuel cell, Computer Physics Communications 200 (2016) 15–26.Does the new version supersede the previous version?: NoReasons for new version: This new version aims to account for additional electrochemical applications.Summary of revisions: The new version employs new code structure designs and is capable of considering two different electric potential fields and two-phase flows.Nature of problem: This software library provides a set of models for simulating electrochemical devices, such as fuel cells and electrolyzers, as well as other similar devices. These systems consist of multiple components with distinct features but are coupled through properties such as temperature, species concentrations, and electric current/potentials. This software utilizes a computational fluid dynamics (CFD) approach to enable the simulation of multiregion and multiphysics problems, accounting for heat and mass transfer, single and two-phase flow, multicomponent diffusion, electron and ion transfer, and electrochemical reactions. This toolbox provides researchers with a powerful tool for studying electrochemical devices in a comprehensive and efficient manner.Solution method: This software utilizes the finite volume method (FVM) to discretize and solve all conserved variables governed by partial differential equations. It employs a variant of the SIMPLE and PISO algorithms, known as PIMPLE, to solve the pressure-velocity coupling. All of the transport equations are solved sequentially, except for the enthalpy equation which is solved in an implicitly coupled manner within the global domain.Additional comments including restrictions and unusual features:•The two-phase flow consists of continuous and dispersed phases, without resolving the phase interfaces.•The two-phase flow is solved with an Eulerian-Eulerian approach.•A local-time-stepping method was typically used in the two-phase solution.•The electrochemical reactions take place in volumetric regions.•Species diffusion is described by Fick's law.

Boundary constrained quadrilateral mesh generation based on domain decomposition and templates

Compared to triangular or mixed meshes, pure quadrilateral meshes generally offer higher accuracy and computational efficiency in numerical simulations. Recently, the main obstacles in the generation of quadrilateral meshes have revolved around the identification of mesh singularities and the subsequent decomposition of the domain. In this study, a novel quadrilateral mesh generation method based on domain decomposition and templates is presented. The basic idea is to decompose the domain by separating the mesh singularities rather than identifying their precise locations. Surfaces composed of a set of surface patches are meshed independently. For each surface patch, the problem domain is divided into several simple polygonal subregions, including quadrangles, triangles, and pentagons, using constrained Delaunay triangulation (CDT) and recursive bisections. Subsequently, mesh templates with a limited number of singularities are employed to rapidly generate high-quality quadrilateral meshes over those subregions. By constraining the boundary discretization of each surface patch, mesh conformability is automatically achieved. An integer linear programming equation is presented to ensure that the total number of boundary nodes on each surface is an even value. Several experimental results are presented and discussed, demonstrating the reliability and efficiency of the proposed method.

Practical considerations for the adoption of Anderson acceleration in nonlinear diffusion accelerated transport

The use of the Anderson Acceleration (AA) method within the context of the coarse mesh finite difference (CMFD)-accelerated neutron transport k-eigenvalue calculation is explored for practical problems. Current application of CMFD only has a linear convergence rate. The AA method is similar to a quasi-Newton method and can improve the convergence rate of fixed-point iterations. We therefore implement AA for the 2D calculation in MPACT and study its performance in pressurized water reactor (PWR) problems. The initial results show that the traditional AA method can improve the convergence rate in a trivial problem and improve the stability of the CMFD method for some problems. However, the success of AA in the practical problems, where simulations with symmetry or domain decomposition, relies on one essential factor–the treatment of iterative angular flux boundary conditions in the AA. Additionally, the efficiency of AA is also affected by the computational cost for solving the optimization problem, and the computational cost of the transport solver and the CMFD solver. To address these issues, we propose a new implementation of AA that considers only the mutligroup scalar flux in the optimization problem, but the angular flux and the scalar flux in the mixing. The new approach achieves better stability and efficiency in practical simulations, and can be explained by the theory of Randomized Numerical Linear Algebra (RandNLA).

Research on electromagnetic scattering and radio wave propagation algorithm based on machine learning in half-space

In this paper, to investigate the problem of radio wave propagation in complex environments, a new algorithm is proposed based on the equivalence principle algorithm and the domain decomposition method to rapidly and accurately predict electromagnetic scattering and radio wave propagation in half-space. First, equivalent surfaces are introduced to decompose the obstacle region and replace the scattering effect of obstacles within the equivalent surfaces with equivalent input and output electromagnetic currents. Then, the operator S, representing the relationship between the input and output equivalent electromagnetic currents on the equivalent surfaces, and the operator T, representing the interactions between the equivalent electromagnetic currents on each equivalent surface, are derived; this allows the calculation process of the overall spatial field in a complex environment to be simplified to the iterative calculation process of operators S and T. To reduce the complexity of calculating S, a neural network embedded with physical information is introduced to replace the calculation process. Finally, the training results are applied to an example and compared with the theoretical numerical results yielded by the method of moments in different cases with obstacles. The results reveal that the new method proposed in this paper is highly accurate and achieves a substantial improvement in calculation speed. Therefore, our proposed algorithm provides a new and reliable method for calculating the spatial field in complex environments.

Seawater temperature and salinity sensing based on in-fiber Michelson-Fabry-Perrot hybrid interferometer employing frequency domain decomposition method

Seawater temperature and salinity sensing based on in-fiber Michelson-Fabry-Perrot hybrid interferometer employing frequency domain decomposition method

A computational framework for pharmaco‐mechanical interactions in arterial walls using parallel monolithic domain decomposition methods

AbstractA computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch‐dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation‐diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja–Smith–Widlund) and RGDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug‐induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed.

LSTM-Based Approach for Stable Identification of Modal Damping Ratio in Building Structures

Modal parameters are used as safety assessment indicators for evaluating the structural integrity of buildings in various ways. In particular, the modal damping ratio plays a crucial role in accurately predicting the serviceability and safety of buildings, starting from the initial design stage. However, the identification results of the modal damping ratio can become unstable due to measurement time, initial configuration conditions used in the analysis, and nonstationary responses included in the structural response. To address the instability issue, this study proposes a long short-term memory-based frequency domain decomposition (FDD-LSTM) method. The FDD-LSTM method utilizes the acceleration response of the building as input data and the modal damping ratio obtained from the FDD method as output data, constructing an LSTM network model for the relationship between the acceleration response and modal damping ratio. The FDD-LSTM method exhibited a discrepancy of less than 0.02% compared to the reference value of the modal damping ratio obtained through free vibration response. Furthermore, when applied to data acquired from an actual building, the method demonstrated a variance of approximately 5%. The proposed FDD-LSTM method is validated for stability performance using a three-degree-of-freedom numerical analysis model, a 3-story steel frame structure model, and a 117-story high-rise building. The FDD-LSTM method, trained on a large dataset, enables generalized estimation and addresses instability issues related to modal damping ratio.

Enhancing response estimation and system identification in structural health monitoring through data-driven approaches

Through the advancement of Data Science methodologies, a new era in output-only identification techniques has been inaugurated, driven by the integration of data-driven methodologies within the realm of Structural Health Monitoring (SHM). This study endeavors to introduce a simplified data-driven approach catering to System Identification (SI) and Response Estimation (RE). This is realized through the utilization of a summation of sine functions, fashioned as a model to harmonize with time domain vibration and acoustic responses. The fidelity of the findings is subsequently authenticated through the application of the Frequency Domain Decomposition (FDD) technique. In addition to the identification process, the proposed approach extends its applicability to predicting time domain responses at novel locations. This augmentation is achieved by harnessing an enhanced methodology founded on the principles of the Dynamic Mode Decomposition (DMD) technique. The veracity of these predicted outcomes is underscored through a comparison with measurements recorded at the same locations, alongside concurrent analysis of DMD-derived results. In order to affirm the efficacy of the proposed methodology, a case study involving a building grappling with enigmatic vibration issues is meticulously selected. The findings underscore that the proposed technique not only adeptly discerns unidentified vibrations without resorting to frequency domain transformation techniques, but also facilitates precise estimation of time domain responses.

A parallel preconditioning Schur complement approach for large scale industrial problems

The purpose of this paper is to introduce a new strategy to improve the convergence and efficiency of the class of domain decomposition known as Schur complement techniques related to interface variables for the simulation of mechanical, electrical and thermal problems in presence of cross points. More precisely, we are interested not only in domain decomposition with two equal parts having the same physical properties but rather in more general splitting components. It is known that in the first case, the optimal convergence with good pre-conditioner is obtained in two iterations and the problem is still challenging in the second case. The primary goal then is to fill part of the gap in such problem domain decomposition techniques and to contribute to solve extremely difficult industrial problems of large scale by using parallel sparse direct solver of the multi-core environment of the whole system and handling each part of the system independently of the change of the mesh or the shifting of the mathematical method of resolution and subsequently, we treat the interface as boundary conditions. The numerical experiments of our algorithm are performed on few models arising from discretization of partial differential equations using Finite Element Method (FEM).

Analytical study on hydrodynamic performance of co-located offshore wind–solar farms

Based on linear potential flow theory, this study investigates the hydrodynamic performance of a co-located farm with an array of floating offshore wind turbines (FOWTs) and floating photovoltaics (FPVs). In this process, to evaluate the wave–structure interaction, domain decomposition and matched eigenfunction method are applied to address the boundary value problem for a complex-shaped co-located farm, and the velocity potential can be decomposed into radiation and diffraction problems. Under the framework of linearized theory, we establish the coupled motion equations by modeling rigid and articulated constraints to evaluate the kinematic response of the FOWTs and FPVs in the co-located farm. For such a system, a co-located farm consisting of an array of OC4-DeepCwind FOWTs and FPVs is proposed and investigated in this study. After running convergence analysis and model validation, the present model is employed to perform a multiparameter effect analysis. Case studies are presented to clarify the effects of solar platform geometric parameters (including column depth, thickness, radius, and total draft), articulated system, and shadow effect on the hydrodynamic behavior of wind and solar platforms. The findings elucidated in this work provide guidance for the optimized design of FPVs and indicate the potential for synergies between wind and solar energy utilization on floating platforms.

Adaptive solution of the domain decomposition+L2-jumps method applied to the neutron diffusion equation on structured meshes

At the core scale, neutron deterministic calculations are usually based on the neutron diffusion equation. Classically, this equation can be recast in a mixed variational form, and then discretized by using the Raviart-Thomas-Nédélec Finite Element. The goal is to extend the Adaptive Mesh Refinement (AMR) strategy previously proposed in [1] to the Domain Decomposition+L2 jumps which allows non conformity at the interface between subdomains. We are able to refine each subdomain independently, which eventually leads to a more optimal refinement. We numerically investigate the improvements made to the AMR strategy.

Efficient and Accurate Simulations of Metamaterials Based on Domain Decomposition and Unit Feature Database

Efficient and Accurate Simulations of Metamaterials Based on Domain Decomposition and Unit Feature Database

Adaptively Placed Multi-Grid Scene Representation Networks for Large-Scale Data Visualization.

Scene representation networks (SRNs) have been recently proposed for compression and visualization of scientific data. However, state-of-the-art SRNs do not adapt the allocation of available network parameters to the complex features found in scientific data, leading to a loss in reconstruction quality. We address this shortcoming with an adaptively placed multi-grid SRN (APMGSRN) and propose a domain decomposition training and inference technique for accelerated parallel training on multi-GPU systems. We also release an open-source neural volume rendering application that allows plug-and-play rendering with any PyTorch-based SRN. Our proposed APMGSRN architecture uses multiple spatially adaptive feature grids that learn where to be placed within the domain to dynamically allocate more neural network resources where error is high in the volume, improving state-of-the-art reconstruction accuracy of SRNs for scientific data without requiring expensive octree refining, pruning, and traversal like previous adaptive models. In our domain decomposition approach for representing large-scale data, we train an set of APMGSRNs in parallel on separate bricks of the volume to reduce training time while avoiding overhead necessary for an out-of-core solution for volumes too large to fit in GPU memory. After training, the lightweight SRNs are used for realtime neural volume rendering in our open-source renderer, where arbitrary view angles and transfer functions can be explored. A copy of this paper, all code, all models used in our experiments, and all supplemental materials and videos are available at https://github.com/skywolf829/APMGSRN.

UAV search coverage under priority of important targets based on multi-location domain decomposition

<abstract> <p>In recent years, the coverage path planning (CPP) of unmanned aerial vehicles (UAVs) has attracted attention in reconnaissance, patrol, and search and rescue efforts, aiming to plan the paths for UAVs to cover a specified area as efficiently as possible. This paper proposes a UAV path fast coverage model to prioritize important targets with domain composition based on the starting point and location of the targets, combined with the domain decomposition strategy of important targets. Considering the constraints of the number of UAVs, the number of operators, and the flight time, the parallel search strategy can plan the coverage scheme with the shortest search time for the search range, and further obtain the coordinate points and path coordinates of the UAV turning. Finally, through multiple simulation experiments in four maps of various islands, the proposed method is verified to have an improved performance compare to the two track path coverage algorithms methods in terms of the coverage efficiency and the time complexity, thus providing a more scientific basis for the path coverage research of multi-target searches.</p> </abstract>

Structural monitoring, FEM updating and performance assessment of a wind turbine

In this study, long-term monitoring of a 900-kW onshore wind turbine with a tubular steel tower of 54 meters high and foundation with 26 reinforced concrete piles was performed based on vibration data. Modal properties such as frequency, mode shape and damping ratios were obtained by Enhanced Frequency Domain Decomposition method. Then, change in modal parameters due to environmental and operational conditions was determined. Modal parameters after cleansing such effects were obtained by multiple linear regression analyses.Finite element model of the wind turbine was developed in ANSYS including piles. Soil-structure interaction was modelled by p-y, t-z and q-z soil springs. Finite element model of the wind turbine was updated based on identified modal parameters.Finally, nonlinear time histories were performed to obtain seismic fragility curves of the structure with limit states being the local buckling under different levels of wind speed. In the context of this study, it was observed that identified modal values had significant scattering and level of wind speed significantly changed the seismic fragility curve of the wind turbine.

Domain Decomposition Methods for Diffusion Problems with Discontinuous Coefficients Revisited

Domain Decomposition Methods for Diffusion Problems with Discontinuous Coefficients Revisited

A Mixed Discretization Scheme for Discontinuous Galerkin Domain Decomposition Method Applied to Surface Integral Equations

A Mixed Discretization Scheme for Discontinuous Galerkin Domain Decomposition Method Applied to Surface Integral Equations

Electrothermal Transient Co-simulation With Domain Decomposition Method for 3-D Complex Integrated Systems

Electrothermal Transient Co-simulation With Domain Decomposition Method for 3-D Complex Integrated Systems