1,260 results on '"domain decomposition method"'
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2. Deep learning-driven domain decomposition (DLD[formula omitted]): A generalizable AI-driven framework for structural analysis
- Author
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Vemparala, Balavignesh, Yang, Ming, and Soghrati, Soheil
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- 2024
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3. Convergence analysis and applicability of a domain decomposition method with nonlocal interface boundary conditions
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Li, Hongru and Papalexandris, Miltiadis V.
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- 2025
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4. A domain decomposition method employing displacement-only partitioned equations for quasi-static structural analysis
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Kang, Seung-Hoon, Park, K.C., González, José A., and Shin, SangJoon
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- 2024
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5. Domain decomposition method based on One-Way approaches for sound propagation in a partially lined duct
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Ruello, Maëlys, Rudel, Clément, Pernet, Sébastien, and Brazier, Jean-Philippe
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- 2024
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6. Solving Stochastic Time-Cost Trade-Off Problems via Modified Double-Loop Procedure with Adaptive Domain Decomposition Method.
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Wang, Jia, Huang, Wei, and Chen, Yahan
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DOMAIN decomposition methods , *STOCHASTIC analysis , *MONTE Carlo method , *GENETIC algorithms , *PROJECT managers - Abstract
Stochastic time-cost trade-off (TCT) problems are of significant concern to project managers because various uncertain factors have to be considered when making appropriate balance between project completion time and cost. In the paper we consider the stochastic TCT problem, where the project completion time (PCT) unreliability is involved and constrained to be less than a prescribed threshold. To tackle the concerned problem, previous studies have implemented the double loop procedure, where a genetic algorithm (GA) is used in the outer loop for optimization, and Monte Carlo simulation (MCS) is used in the inner loop for examining the unreliability constraint. The original double loop procedure is computationally inefficient, taking hours or days even for a small to medium project. The present study proposes an efficient simulation method, referred to as adaptive domain decomposition method (DDM), to replace MCS for credibly examining the unreliability constraint. By modifying the double loop procedure with adaptive DDM, the computational resources can be effectively allocated, and the computational efficiency can be greatly improved. As shown in the illustrative example, the modified procedure significantly outperforms the original procedure, and it is hundreds of times faster to obtain similar optimization results. With the great efficiency improvement, this study contributes to the widespread acceptance of stochastic TCT analysis in practical applications. [ABSTRACT FROM AUTHOR]
- Published
- 2025
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7. Exact analytic technique for designing controller architecture in multi-axis active magnetic bearings with rotor eccentricities.
- Author
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Dutta, Debarghya, Debnath, Sukanta, and Biswas, Pabitra Kumar
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MAGNETIC bearings , *DOMAIN decomposition methods , *ROTOR dynamics , *MAGNETIC fields , *ROTOR bearings - Abstract
AbstractMulti-coil active magnetic bearing systems require an efficient controller design to maintain stability, maximize performance, and improve flexibility in high-speed transport systems, particularly those used in electric cars, military, and aerospace. By employing Fourier-based frameworks rather than conventional Laplace-based methods, the work reported here simplifies the AMBs controllers, offering more flexibility to complex dynamics and adaptability to non-linearity. For computational and mathematical brevity, the entire formulation has been linearized around a specific range of uncertainty in this work. The magnetic field pattern with rotor eccentricities is characterized by using a subdomain technique and a perturbation methodology. Complex magnetic field formulations are obtained by the estimation of zeroth and first-order formulae in polar coordinates. For every coil, predictive model-based interpolation functions are constructed and optimal controller settings for stability are found by eigenvalue evaluation. The study enhances accuracy and effectiveness by validating these analytical methods against numerical results, offering deeper insights into rotor dynamics and controller adjustments. [ABSTRACT FROM AUTHOR]
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- 2024
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8. Multi-Scale Multi-Domain Hybrid Finite Element Modeling of Light Propagation
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Jingwei Wang, Zhanwen Wang, Lida Liu, and Yuntian Chen
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multi-scale modeling ,finite element method ,domain decomposition method ,slow varying beam envelope ,Electricity and magnetism ,QC501-766 - Abstract
We revisit finite element method of modeling multi-scale photonic/electromagnetic devices via the proposed beam basis function, in combination with domain decompositions. Our approach ensures mathematical and physical consistency, can also handle multi-scale computational tasks efficiently with the assistance of the damping block-Jacobi iterative solver. By implementing the first-order Robin transmission condition at the interfaces between neighboring subdomains and introducing the dual “current” variables, we can significantly reduce the computational burden and communication data volume during the iterative solving process. The theoretical foundation and detailed implementation procedures are presented, accompanied with two representative examples. The first example is a refractive-diffractive hybrid optical system with feature size contrast up to 104, while the second example is the free surface optical system wherein the geometric ray tracing algorithm is inadequate. The obtained results for the two examples show excellent agreement with the standard finite element method (standard FEM) with significantly reducing the number of meshes required for computation and memory usages to nearly one-fifth. Since the computational time is inversely proportional to the number of decomposed subdomains (N) under the parallel computing configuration, the computational time in our work is approximately reduced to \begin{document}${1}/{3N}$\end{document} of that using standard FEM for the two examples.
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- 2024
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9. A ROBUST TWO-LEVEL OVERLAPPING PRECONDITIONER FOR DARCY FLOW IN HIGH-CONTRAST MEDIA.
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CHANGQING YE, SHUBIN FU, CHUNG, ERIC T., and JIZU HUANG
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DOMAIN decomposition methods , *DARCY'S law , *PARTIAL differential equations , *FINITE element method , *CONTRAST media , *SCHWARZ function - Abstract
In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element method for discretizing the partial differential equation by Darcy's law with the no-flux boundary condition and is then followed by a velocity elimination technique to yield a linear algebraic system with only unknowns of pressure. Then, our main objective is to design a robust and efficient domain decomposition preconditioner for this system, which is accomplished by engineering a multiscale coarse space that is capable of characterizing high-contrast features of the permeability field. A generalized eigenvalue problem is solved in each nonoverlapping coarse element in a communication-free manner to form the global solver, which is accompanied by local solvers originated from additive Schwarz methods but with a non-Galerkin discretization to derive the two-level preconditioner. We provide a rigorous analysis that indicates that the condition number of the preconditioned system could be bounded above with several assumptions. Extensive numerical experiments with various types of three-dimensional high-contrast models are exhibited. In particular, we study the robustness against the contrast of the media as well as the influences of numbers of eigenfunctions, oversampling sizes, and subdomain partitions on the efficiency of the proposed preconditioner. Strong and weak scalability performances are also examined. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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10. Two-grid Domain Decomposition Method for Coupling of Fluid Flow with Porous Media Flow.
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Hao Zheng and Liyun Zuo
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DOMAIN decomposition methods , *DARCY'S law , *NAVIER-Stokes equations , *HYDRAULIC couplings , *FLUID flow - Abstract
This paper introduces a hybrid approach, merging the two-grid and domain decomposition strategies, to address the coupled Navier-Stokes-Darcy challenge, which is then elaborated and examined. First, the current Robin boundary condition-based domain decomposition technique is used to get the approximate solution on the coarse grid. Following the substitution of certain interface elements with coarse meshbased functions, an improved fine grid problem is obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2024
11. An Extensible Approach to Organizing Parallel Computations in the Software Package for the LS-STAG Simulation in Coupled Aerohydroelastic Problems
- Author
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Marchevsky, Ilia, Puzikova, Valeria, Ghosh, Ashish, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Sokolinsky, Leonid, editor, Zymbler, Mikhail, editor, Voevodin, Vladimir, editor, and Dongarra, Jack, editor
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- 2024
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12. Experimental Study of the Efficiency of Parallel Solution of Three-Dimensional Boundary-Value Problems on Quasi-Structured Grids with Irregular Subgrids
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Korneev, Vladimir, Sveshnikov, Viktor, Ghosh, Ashish, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Sokolinsky, Leonid, editor, Zymbler, Mikhail, editor, Voevodin, Vladimir, editor, and Dongarra, Jack, editor
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- 2024
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13. Improving Deep Learning-Based Digital Image Correlation with Domain Decomposition Method.
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Chi, Y., Liu, Y., and Pan, B.
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DOMAIN decomposition methods , *DEEP learning , *DIGITAL image correlation - Abstract
Background: Deep learning-based digital image correlation (DL-based DIC) has gained increasing attention in the last two years. However, existing DL-based DIC algorithms are impractical because their application scenarios are mostly limited to small deformations. Objective: To enable the use of DL-based DIC in real-world general experimental mechanics scenarios that would involve large deformations and rotations, we propose to improve DL-based DIC with the domain decomposition method (DDM). Methods: In the improved method, the region of interest is divided into subimages, and subimages are pre-aligned using the preregistered control points to effectively eliminate the large deformation components. The residual deformations in each subimage are small and limited, which can be well extracted using existing DL-based DIC methods. Results: Through synthesized and real-world experiments, the improved DL-based DIC method can achieve high-accuracy pixelwise matching in practical applications with strong robustness and high computational efficiency. Conclusions: The improved DL-based DIC combines the advantages of traditional and DL-based DIC methods but overcomes the limitations, greatly improving the robustness and applicability of existing DL-based methods. [ABSTRACT FROM AUTHOR]
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- 2024
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14. A Multilevel Approach for Direct Core Calculation Schemes.
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Galia, Antonio
- Abstract
AbstractA method of dynamic homogenization was recently proposed as an alternative technique for three-dimensional (3D) core calculations using a direct approach. This technique allows for producing homogenization parameters for a subdomain within the core at its actual state, and offers the advantage of avoiding off-line calculations, cross-section interpolations, and expensive 3D transport calculations. The methodology has shown a remarkable reduction in computational cost compared to 3D transport. However, the application of direct calculation schemes in multiphysics and multicycle problems still demands an extensive use of computational resources. Within the framework of traditional two-step calculations, several multilevel schemes have been developed to accelerate lattice calculations for the generation of the multiparameter cross-section libraries.With a similar objective, this work investigates how the multilevel approach can be applied within the framework of direct calculation schemes and discusses how depletion calculations may be performed. The objective is to enhance their performance and reduce memory requirements in favor of a high-fidelity model of the matter behavior in the reactor. We have then identified suitable flux solvers for each level and explored various homogenization options. We tested the methodology in a 3D pressurized water reactor core problem inspired by the TVA Watts Bar Unit 1 Multi-Physics Multi-Cycle OECD/NEA Benchmark, and performed a comparative analysis to assess the accuracy and computational efficiency of these new calculation schemes against direct single-level calculations and a two-step calculation based on pin-by-pin homogenization, as well as Monte Carlo simulations.Our analysis proves that the computational resources required to solve the full-core problem using a multilevel scheme are significantly reduced, and the best computational features are provided by multilevel dynamic homogenization. Furthermore, we observed that the multilevel approach not only allows for speedup, but can also be advantageously applied in order to improve the accuracy of the final solution of a calculation scheme when the core solver relies on an approximate transport operator. [ABSTRACT FROM AUTHOR]
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- 2024
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15. SOLUTION TO A COUPLED PROBLEM OF THERMOMECHANICAL CONTACT OF FUEL ELEMENTS.
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Galanin, M. P. and Rodin, A. S.
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DOMAIN decomposition methods , *FINITE element method - Abstract
A problem of mathematical simulation of a fuel element region, including many fuel pellets and a cladding fragment, is considered in an axisymmetric formulation. It is assumed that the cladding is a thermoelastic-plastic body and that the pellet is a thermoelastic body with account for cracking of the material. Different variants of the domain decomposition method are used to numerically simulate the thermal and mechanical contact of pellets with each other and with the cladding. Calculation results are presented, in which the region containing ten pellets reaches a nominal power and the effect of pellet cracking on the thermomechanical state of the fuel element is estimated. [ABSTRACT FROM AUTHOR]
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- 2024
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16. An efficient parallel solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method.
- Author
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Hao, Shourong and Shen, Yongxing
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DOMAIN decomposition methods ,LAGRANGE multiplier ,PARALLEL algorithms ,DEGREES of freedom ,PHASE coding - Abstract
The phase field approach to fracture becomes popular for complicated fracture problems in recent years. However, its widespread application is hindered by its high computational cost. In this article, we propose an efficient parallel explicit‐implicit solution scheme for the phase field approach to dynamic fracture based on a domain decomposition method, specifically, the dual‐primal finite element tearing and interconnecting (FETI‐DP) method. In this scheme, the displacement field is updated by an explicit algorithm in parallel, and the phase field is implicitly solved by the FETI‐DP method. In particular, Lagrange multipliers are introduced to ensure the interface continuity of the phase field. In the computational process, the information exchange among subdomains merely exists in a few substeps, which renders the cost for communication very small. Moreover, the size of equations to be solved is proportional to the total area of subdomain interfaces, which is significantly reduced compared with a typical single‐domain solution procedure. The solution scheme is able to perform phase field simulations with a million of degrees of freedom using only 0.034 core hours per load step, and has flexible extensibility for existing phase field codes. Several numerical examples demonstrate the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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17. A Novel Domain Decomposition Method for Eigenvalue Problems.
- Author
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Xu, Fei, Chen, Shuangshuang, and Luo, Fusheng
- Abstract
A novel domain decomposition method is proposed in this paper to solve eigenvalue problems. Both the simple and multiple eigenvalues are considered in algorithm design and theoretical analysis. The key thought is to transform the eigenvalue problem into a number of linear boundary value problems in a multilevel space sequence and some small-scale eigenvalue problems in a low-dimensional correction space. Then some well-developed domain decomposition methods for linear boundary value problem can be directly used to resolve eigenvalue problems. Through rigorous theoretical analysis and numerical experiments, we can find the presented novel domain decomposition algorithm for eigenvalue problems can derive the same solving efficiency and parallel scalability as that for linear boundary value problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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18. Parallel Algorithm for Incompressible Flow Simulation Based on the LS-STAG and Domain Decomposition Methods
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Puzikova, Valeria, Marchevsky, Ilia, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Voevodin, Vladimir, editor, Sobolev, Sergey, editor, Yakobovskiy, Mikhail, editor, and Shagaliev, Rashit, editor
- Published
- 2023
- Full Text
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19. Orlicz estimates for parabolic Schrödinger operators with non-negative potentials on nilpotent Lie groups
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Kelei Zhang
- Subjects
nilpotent lie group ,orlicz space ,parabolic schrödinger operator ,non-negative potential ,domain decomposition method ,Mathematics ,QA1-939 - Abstract
In this paper, we study the Orlicz estimates for the parabolic Schrödinger operator $ L = {\partial _t} - {\Delta _X} + V, $ where the nonnegative potential $ V $ belongs to a reverse Hölder class on nilpotent Lie groups $ {\Bbb G} $ and $ {\Delta _X} $ is the sub-Laplace operator on $ {\Bbb G} $. Under appropriate growth conditions of the Young function, we obtain the regularity estimates of the operator $ L $ in the Orlicz space by using the domain decomposition method. Our results generalize some existing ones of the $ L^{p} $ estimates.
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- 2023
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20. Domain Decomposition with Neural Network Interface Approximations for time-harmonic Maxwell's equations with different wave numbers
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Tobias Knoke, Sebastian Kinnewig, Sven Beuchler, Ayhan Demircan, Uwe Morgner, and Thomas Wick
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time-harmonic maxwell's equations ,machine learning ,feedforward neural network ,domain decomposition method ,Applied mathematics. Quantitative methods ,T57-57.97 ,Mathematics ,QA1-939 - Abstract
In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface conditions between the subdomains. The advantage is that the interface condition can be updated without recomputing the Maxwell system at each step. The main part consists of a detailed description of the construction of the neural network for domain decomposition and the training process. To substantiate this proof of concept, we investigate a few subdomains in some numerical experiments with low frequencies. Therein the new approach is compared to a classical domain decomposition method. Moreover, we highlight current challenges of training and testing with different wave numbers and we provide information on the behaviour of the neural-network, such as convergence of the loss function, and different activation functions.
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- 2023
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21. A Schwarz alternating method for an evolution convection problem.
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Martínez, D., Pla, F., Herrero, H., and Fernández-Pérez, A.
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DOMAIN decomposition methods , *NAVIER-Stokes equations , *FINITE differences , *COLLOCATION methods , *NONLINEAR equations , *PRANDTL number , *SCHWARZ function - Abstract
A study of an alternating Schwarz domain decomposition method for a time evolution Rayleigh-Bénard problem is presented. The model equations are Navier-Stokes, continuity and heat equations in the case of infinite Prandtl number in a two-dimensional rectangular domain. The nonlinear evolution problem is dealt with an order two finite differences scheme in time and a collocation method in space. Each step in the evolution problem is solved with a Schwarz domain decomposition method. The domain is split into several subdomains with appropriate interface conditions. Their convergence properties are studied theoretically in a simplified domain divided in two subdomains. The convergence rate is less than one when an overlap is considered. The numerical resolution of the problem confirms the theoretical results. The number of subdomains in the horizontal direction can be increased indefinitely. A benchmark with numerical solutions obtained with other methods validates the method. Convergence is achieved for large spatial grids in the x axis, which are inabordable for the standard Legendre collocation method. Other advantage of this methodology is parallelization. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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22. Large-Scale Cluster Parallel Strategy for Regularized Lattice Boltzmann Method with Sub-Grid Scale Model in Large Eddy Simulation.
- Author
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Liu, Zhixiang, Chen, Yuanji, Xiao, Wenjun, Song, Wei, and Li, Yu
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LARGE eddy simulation models ,REYNOLDS number ,FLUID flow ,DOMAIN decomposition methods ,MODELS & modelmaking ,LATTICE Boltzmann methods ,INCOMPRESSIBLE flow - Abstract
As an improved method of the lattice Boltzmann method (LBM), the regularized lattice Boltzmann method (RLBM) has been widely used to simulate fluid flow. For solving high Reynolds number problems, large eddy simulation (LES) and RLBM can be combined. The computation of fluid flow problems often requires a large number of computational grids and large-scale parallel clusters. Therefore, the high scalability parallel algorithm of RLBM with LES on a large-scale cluster has been proposed in this paper. The proposed parallel algorithm can solve complex flow problems with large-scale Cartesian grids and high Reynolds numbers. In order to achieve computational load balancing, the domain decomposition method (DDM) has been used in large-scale mesh generation. Three mesh generation strategies are adopted, namely 1D, 2D and 3D. Then, the buffer on the grid interface is introduced and the corresponding 1D, 2D and 3D parallel data exchange strategies are proposed. For the 3D lid-driven cavity flow and incompressible flow around a sphere under a high Reynolds number, the given parallel algorithm is analyzed in detail. Experimental results show that the proposed parallel algorithm has a high scalability and accuracy on hundreds of thousands of cores. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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- View/download PDF
23. A combination of Kohn-Vogelius and DDM methods for a geometrical inverse problem.
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Chaabane, Slim, Haddar, Houssem, and Jerbi, Rahma
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INVERSE problems , *DOMAIN decomposition methods , *ELECTRIC conductivity , *ELECTRICAL conductivity measurement - Abstract
We consider the inverse geometrical problem of identifying the discontinuity curve of an electrical conductivity from boundary measurements. This standard inverse problem is used as a model to introduce and study a combined inversion algorithm coupling a gradient descent on the Kohn-Vogelius cost functional with a domain decomposition method that includes the unknown curve in the domain partitioning. We prove the local convergence of the method in a simplified case and numerically show its efficiency for some two dimensional experiments. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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- View/download PDF
24. A GenEO Domain Decomposition method for Saddle Point problems
- Author
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Nataf, Frédéric and Tournier, Pierre-Henri
- Subjects
domain decomposition method ,nearly incompressible elasticity ,high performance computing ,saddle point problem ,coarse space ,multiscale finite element ,Schur complement ,Materials of engineering and construction. Mechanics of materials ,TA401-492 - Abstract
We introduce an adaptive element-based domain decomposition (DD) method for solving saddle point problems defined as a block two by two matrix. The algorithm does not require any knowledge of the constrained space. We assume that all sub matrices are sparse and that the diagonal blocks are spectrally equivalent to a sum of positive semi definite matrices. The latter assumption enables the design of adaptive coarse space for DD methods that extends the GenEO theory (Spillane et al., 2014) to saddle point problems. Numerical results on three dimensional elasticity problems for steel-rubber structures discretized by a finite element with continuous pressure are shown for up to one billion degrees of freedom.
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- 2023
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25. Parallel-in-space-and-time finite-element analysis of electric machines using time step overlapping in a massively parallel computing environment
- Author
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Takahashi, Yasuhito, Fujiwara, Koji, and Iwashita, Takeshi
- Published
- 2023
- Full Text
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26. Orlicz estimates for parabolic Schrödinger operators with non-negative potentials on nilpotent Lie groups.
- Author
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Zhang, Kelei
- Subjects
PARABOLIC operators ,SCHRODINGER operator ,DOMAIN decomposition methods ,NILPOTENT Lie groups ,ORLICZ spaces - Abstract
In this paper, we study the Orlicz estimates for the parabolic Schrödinger operator where the nonnegative potential belongs to a reverse Hölder class on nilpotent Lie groups and is the sub-Laplace operator on. Under appropriate growth conditions of the Young function, we obtain the regularity estimates of the operator in the Orlicz space by using the domain decomposition method. Our results generalize some existing ones of the estimates. In this paper, we study the Orlicz estimates for the parabolic Schrödinger operator where the nonnegative potential belongs to a reverse Hölder class on nilpotent Lie groups and is the sub-Laplace operator on. Under appropriate growth conditions of the Young function, we obtain the regularity estimates of the operator in the Orlicz space by using the domain decomposition method. Our results generalize some existing ones of the estimates. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
27. Fast Multi-Grid Methods for Minimizing Curvature Energies.
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Zhang, Zhenwei, Chen, Ke, Tang, Ke, and Duan, Yuping
- Subjects
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DOMAIN decomposition methods , *GAUSSIAN curvature , *IMAGE denoising , *IMAGE reconstruction , *IMAGE processing - Abstract
The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners, and contrast. However, the dilemma between restoration quality and computational efficiency is an essential roadblock for high-order methods. In this paper, we propose fast multi-grid algorithms for minimizing both mean curvature and Gaussian curvature energy functionals without sacrificing accuracy for efficiency. Unlike the existing approaches based on operator splitting and the Augmented Lagrangian method (ALM), no artificial parameters are introduced in our formulation, which guarantees the robustness of the proposed algorithm. Meanwhile, we adopt the domain decomposition method to promote parallel computing and use the fine-to-coarse structure to accelerate convergence. Numerical experiments are presented on image denoising, CT, and MRI reconstruction problems to demonstrate the superiority of our method in preserving geometric structures and fine details. The proposed method is also shown effective in dealing with large-scale image processing problems by recovering an image of size $1024\times 1024$ within 40s, while the ALM-based method requires around 200s. [ABSTRACT FROM AUTHOR]
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- 2023
- Full Text
- View/download PDF
28. Modeling and a Domain Decomposition Method with Finite Element Discretization for Coupled Dual-Porosity Flow and Navier–Stokes Flow.
- Author
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Hou, Jiangyong, Hu, Dan, Li, Xuejian, and He, Xiaoming
- Abstract
In this paper, we first propose and analyze a steady state Dual-Porosity-Navier–Stokes model, which describes both Dual-Porosity flow and free flow (governed by Navier–Stokes equation) coupled through four interface conditions, including the Beavers–Joseph interface condition. Then we propose a domain decomposition method for efficiently solving such a large complex system. Robin boundary conditions are used to decouple the Dual-Porosity equations from the Navier–Stokes equations in the coupled system. Based on the two decoupled sub-problems, a parallel Robin-Robin domain decomposition method is constructed and then discretized by finite elements. We analyze the convergence of the domain decomposition method with the finite element discretization and investigate the effect of Robin parameters on the convergence, which also provide instructions for how to choose the Robin parameters in practice. Three cases of Robin parameters are studied, including a difficult case which was not fully addressed in the literature, and the optimal geometric convergence rate is obtained. Numerical experiments are presented to verify the theoretical conclusions, illustrate how the theory can provide instructions on choosing Robin parameters, and show the features of the proposed model and domain decomposition method. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
29. High‐performance computing of 3D blasting wave propagation in underground rock cavern by using 4D‐LSM on TianHe‐3 prototype E class supercomputer
- Author
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Meng Fu and Gaofeng Zhao
- Subjects
domain decomposition method ,lattice spring model ,parallel computing ,wave propagation ,Engineering geology. Rock mechanics. Soil mechanics. Underground construction ,TA703-712 - Abstract
Abstract Parallel computing assigns the computing model to different processors on different devices and implements it simultaneously. Accordingly, it has broad applications in the numerical simulation of geotechnical engineering and underground engineering, of which models are always large‐scale. With parallel computing, the computing time or the memory requirements will be reduced by splitting the original domain of the numerical model into many subdomains, which is thus named as the domain decomposition method. In this study, a cubic and equal volume domain decomposition strategy was utilized to realize the parallel computing on the distributed memory system of four‐dimensional lattice spring model (4D‐LSM) based on the message passing interface. With a more efficient communication strategy introduced, this study aimed at operating an one‐billion‐particle model on a supercomputer platform. The preprocessing procedure of the parallelized 4D‐LSM was restructured and the particle generation strategy suitable for the supercomputer platform was employed to minimize the time consumption in preprocessing and calculation. On this basis, numerical calculations were performed on TianHe‐3 prototype E class supercomputer at the National Supercomputer Center in Tianjin. Two field‐scale three‐dimensional blasting wave propagation models were carried out, of which the numerical results verify the computing power and the advantage of the parallelized 4D‐LSM in the simulation of large‐scale three‐dimension models. Subsequently, the time complexity and spatial complexity of 4D‐LSM and other particle discrete element methods were analyzed.
- Published
- 2022
- Full Text
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30. Reduced-order models for array structures mounted on platforms with parameters variations.
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Fu, Kunpeng, Shao, Hanru, Li, Minhua, and Hu, Jun
- Subjects
- *
REDUCED-order models , *DOMAIN decomposition methods - Abstract
A hybrid model order reduction (MOR) method is developed to calculate the electromagnetic characteristic of array structures mounted on platforms with parameters variations. The reduced-order model (ROM) of the platform is generated as a reduced-order input-output matrix during the offline stage. Using the equivalence principle algorithm (EPA), the ROM of array is generated by transferring the unknowns on the elements to equivalence surfaces. The frequency and material independent reactions (FMIR) method is applied to support the sweep of array material parameters. In the online stage, when the array positions vary in the input region, both of the array and platform ROMs can be used repeatedly. When the array materials vary in the input region, the platform ROM and geometry dependent matrices of EPA are reusable. Therefore, the computational cost can be reduced significantly. Comparing the proposed method to commercial solver, two numerical results are given to show the efficiency. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
31. Transmission operators for the non-overlapping Schwarz method for solving Helmholtz problems in rectangular cavities.
- Author
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Marsic, Nicolas, Geuzaine, Christophe, and De Gersem, Herbert
- Subjects
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PROBLEM solving , *DOMAIN decomposition methods , *NOISE , *HELMHOLTZ equation , *THREE-dimensional modeling - Abstract
In this paper we discuss different transmission operators for the non-overlapping Schwarz method which are suited for solving the time-harmonic Helmholtz equation in cavities (i.e. closed domains which do not feature an outgoing wave condition). Such problems are heavily impacted by back-propagating waves which are often neglected when devising optimized transmission operators for the Schwarz method. This work explores new operators taking into account those back-propagating waves and compares them with well-established operators neglecting these contributions. Notably, this paper focuses on the case of rectangular cavities, as the optimal (non-local) transmission operator can be easily determined. Nonetheless, deviations from this ideal geometry are considered as well. In particular, computations of the acoustic noise in a three-dimensional model of the helium vessel of a beamline cryostat with optimized Schwarz schemes are discussed. Those computations show a reduction of 46% in the iteration count, when comparing an operator optimized for cavities with those optimized for unbounded problems. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
32. MULTILEVEL SPECTRAL DOMAIN DECOMPOSITION.
- Author
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BASTIAN, PETER, SCHEICHL, ROBERT, SEELINGER, LINUS, and STREHLOW, ARNE
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POSITIVE systems , *GALERKIN methods , *LINEAR systems , *FINITE element method , *PROBLEM solving , *SCHWARZ function - Abstract
Highly heterogeneous, anisotropic coefficients, e.g., in the simulation of carbon-Fiber composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer from severe memory requirements and limited parallel scalability, while iterative solvers in general lack robustness. Two-level spectral domain decomposition methods can provide such robustness for symmetric positive definite linear systems by using coarse spaces based on independent generalized eigenproblems in the subdomains. Rigorous condition number bounds are independent of mesh size, number of subdomains, and coefficient contrast. However, their parallel scalability is still limited by the fact that (in order to guarantee robustness) the coarse problem is solved via a direct method. In this paper, we introduce a multilevel variant in the context of subspace correction methods and provide a general convergence theory for its robust convergence for abstract, elliptic variational problems. Assumptions of the theory are verified for conforming as well as for discontinuous Galerkin methods applied to a scalar diffusion problem. Numerical results illustrate the performance of the method for two- and three-dimensional problems and for various discretization schemes, in the context of scalar diffusion and linear elasticity. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
33. An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method.
- Author
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Chen, Jia-Fen, Gu, Xian-Ming, Li, Liang, and Zhou, Ping
- Subjects
- *
DOMAIN decomposition methods , *KRYLOV subspace , *LINEAR systems - Abstract
An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on a triangular mesh of the computational domain. The discretized linear system of the HDG method on each subdomain is solved by a sparse direct solver. The solution of the interface linear system in the domain decomposition framework is accelerated by a Krylov subspace method. We study the spectral radius of the iteration matrix of the Schwarz method for the LORM problems, and thus propose an optimized parameter for the transmission condition, which is different from that for the classical electromagnetic problems. The numerical results show that the proposed method is effective. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
34. Domain decomposition and upscaling technique for metascreens
- Author
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Leumüller, Michael, Hollaus, Karl, and Schöberl, Joachim
- Published
- 2022
- Full Text
- View/download PDF
35. Pairing GIS and Distributed Hydrological Models Using MATLAB
- Author
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Hariri, Sleimane, Weill, Sylvain, Gustedt, Jens, Charpentier, Isabelle, Pisello, Anna Laura, Editorial Board Member, Hawkes, Dean, Editorial Board Member, Bougdah, Hocine, Editorial Board Member, Rosso, Federica, Editorial Board Member, Abdalla, Hassan, Editorial Board Member, Boemi, Sofia-Natalia, Editorial Board Member, Mohareb, Nabil, Editorial Board Member, Mesbah Elkaffas, Saleh, Editorial Board Member, Bozonnet, Emmanuel, Editorial Board Member, Pignatta, Gloria, Editorial Board Member, Mahgoub, Yasser, Editorial Board Member, De Bonis, Luciano, Editorial Board Member, Kostopoulou, Stella, Editorial Board Member, Pradhan, Biswajeet, Editorial Board Member, Abdul Mannan, Md., Editorial Board Member, Alalouch, Chaham, Editorial Board Member, O. Gawad, Iman, Editorial Board Member, Nayyar, Anand, Editorial Board Member, Amer, Mourad, Series Editor, Chenchouni, Haroun, editor, Chaminé, Helder I., editor, Khan, Md Firoz, editor, Merkel, Broder J., editor, Zhang, Zhihua, editor, Li, Peiyue, editor, Kallel, Amjad, editor, and Khélifi, Nabil, editor
- Published
- 2022
- Full Text
- View/download PDF
36. CONVERGENCE ANALYSIS OF NEWTON-SCHUR METHOD FOR SYMMETRIC ELLIPTIC EIGENVALUE PROBLEM.
- Author
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NIAN SHAO and WENBIN CHEN
- Subjects
- *
EIGENVALUES , *FINITE element method , *HILBERT space , *SCHWARZ function , *DOMAIN decomposition methods - Abstract
In this paper, we consider the Newton-Schur method in Hilbert space and obtain quadratic convergence. For the symmetric elliptic eigenvalue problem discretized by the standard finite element method and nonoverlapping domain decomposition method, we use the Steklov-Poincaré operator to reduce the eigenvalue problem on the domain Ω into the nonlinear eigenvalue subproblem on Γ, which is the union of subdomain boundaries. We prove that the convergence rate for the Newton-Schur method is ∈N ≤ C∈7#178;, where the constant C is independent of the fine mesh size h and coarse mesh size H, and ∈N and ∈ are errors after and before one iteration step, respectively. For one specific inner product on Γ, a sharper convergence rate is obtained, and we can prove that ∈N ≤ C H²(1 + ln(H/h))²∈². Numerical experiments confirm our theoretical analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
37. A Schwarz waveform relaxation method for time-dependent space fractional Schrödinger/heat equations.
- Author
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Antoine, Xavier and Lorin, Emmanuel
- Subjects
- *
HEAT equation , *DOMAIN decomposition methods , *SCHRODINGER equation , *NONLINEAR Schrodinger equation - Abstract
This paper is dedicated to the derivation and analysis of a Schwarz waveform relaxation domain decomposition method for solving time-dependent linear/nonlinear space fractional Schrödinger and heat equations. Along with the details of the derivation of the method and some mathematical properties, we also propose some illustrating numerical experiments and conjectures on the rate of convergence of the method. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
38. Resilient asynchronous primal Schur method.
- Author
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Gbikpi-Benissan, Guillaume and Magoulès, Frédéric
- Subjects
- *
DOMAIN decomposition methods , *SCHUR complement , *INTERIOR-point methods - Abstract
This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson's and linear elasticity problems. The asynchronous Schur solver outperformed the classical conjugate-gradient-based one in case of computing node failures. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
39. Comparative Efficiency Analysis of MPI Blocking and Non-blocking Communications with Coarray Fortran
- Author
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Reshetova, Galina, Cheverda, Vladimir, Koinov, Vitaly, Filipe, Joaquim, Editorial Board Member, Ghosh, Ashish, Editorial Board Member, Prates, Raquel Oliveira, Editorial Board Member, Zhou, Lizhu, Editorial Board Member, Voevodin, Vladimir, editor, and Sobolev, Sergey, editor
- Published
- 2021
- Full Text
- View/download PDF
40. Comparative Study on the 4-Stage Series-Connected Fast Linear Transformer Driver with Common- and Independent-Induction Cavity
- Author
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Qiu, Hao, Wang, Shuhong, Angrisani, Leopoldo, Series Editor, Arteaga, Marco, Series Editor, Panigrahi, Bijaya Ketan, Series Editor, Chakraborty, Samarjit, Series Editor, Chen, Jiming, Series Editor, Chen, Shanben, Series Editor, Chen, Tan Kay, Series Editor, Dillmann, Rüdiger, Series Editor, Duan, Haibin, Series Editor, Ferrari, Gianluigi, Series Editor, Ferre, Manuel, Series Editor, Hirche, Sandra, Series Editor, Jabbari, Faryar, Series Editor, Jia, Limin, Series Editor, Kacprzyk, Janusz, Series Editor, Khamis, Alaa, Series Editor, Kroeger, Torsten, Series Editor, Liang, Qilian, Series Editor, Martín, Ferran, Series Editor, Ming, Tan Cher, Series Editor, Minker, Wolfgang, Series Editor, Misra, Pradeep, Series Editor, Möller, Sebastian, Series Editor, Mukhopadhyay, Subhas, Series Editor, Ning, Cun-Zheng, Series Editor, Nishida, Toyoaki, Series Editor, Pascucci, Federica, Series Editor, Qin, Yong, Series Editor, Seng, Gan Woon, Series Editor, Speidel, Joachim, Series Editor, Veiga, Germano, Series Editor, Wu, Haitao, Series Editor, Zhang, Junjie James, Series Editor, Chen, Weijiang, editor, Yang, Qingxin, editor, Wang, Laili, editor, Liu, Dingxin, editor, Han, Xiaogang, editor, and Meng, Guodong, editor
- Published
- 2021
- Full Text
- View/download PDF
41. Large-Scale Cluster Parallel Strategy for Regularized Lattice Boltzmann Method with Sub-Grid Scale Model in Large Eddy Simulation
- Author
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Zhixiang Liu, Yuanji Chen, Wenjun Xiao, Wei Song, and Yu Li
- Subjects
parallel computing ,regularized lattice Boltzmann method ,large eddy simulation ,domain decomposition method ,Technology ,Engineering (General). Civil engineering (General) ,TA1-2040 ,Biology (General) ,QH301-705.5 ,Physics ,QC1-999 ,Chemistry ,QD1-999 - Abstract
As an improved method of the lattice Boltzmann method (LBM), the regularized lattice Boltzmann method (RLBM) has been widely used to simulate fluid flow. For solving high Reynolds number problems, large eddy simulation (LES) and RLBM can be combined. The computation of fluid flow problems often requires a large number of computational grids and large-scale parallel clusters. Therefore, the high scalability parallel algorithm of RLBM with LES on a large-scale cluster has been proposed in this paper. The proposed parallel algorithm can solve complex flow problems with large-scale Cartesian grids and high Reynolds numbers. In order to achieve computational load balancing, the domain decomposition method (DDM) has been used in large-scale mesh generation. Three mesh generation strategies are adopted, namely 1D, 2D and 3D. Then, the buffer on the grid interface is introduced and the corresponding 1D, 2D and 3D parallel data exchange strategies are proposed. For the 3D lid-driven cavity flow and incompressible flow around a sphere under a high Reynolds number, the given parallel algorithm is analyzed in detail. Experimental results show that the proposed parallel algorithm has a high scalability and accuracy on hundreds of thousands of cores.
- Published
- 2023
- Full Text
- View/download PDF
42. The collocation spectral method with domain decomposition for radiative heat transfer in two-dimensional enclosures.
- Author
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Zhou, Rui-Rui, Sun, Ya-Song, and Li, Ben-Wen
- Subjects
- *
COLLOCATION methods , *DECOMPOSITION method , *SUBSTRUCTURING techniques , *HEAT transfer , *HEAT radiation & absorption , *BENCHMARK problems (Computer science) , *RADIATIVE transfer equation - Abstract
In this paper, the collocation spectral method (CSM) combined with domain decomposition method is developed to solve the radiative transfer equation in two-dimensional irregular domains. Three benchmark problems consist of the square enclosure, the L-shaped enclosure and the square enclosure with a centered obstruction are solved and compared with the published data to validate the ability of present developed method. The comparison shows good agreements and indicates that the method has a good accuracy for all problems. Then, the performances of influence matrix technique and iterative substructuring technique to exchange the radiative information between subdomains are compared. It is found that, in the serial computations, the computational cost of influence matrix technique is hundreds of times more expensive than that of iterative substructuring technique. The high cost of influence matrix technique is due to that the radiative intensity is a high dimensional variable with angular dependence, and tremendous subproblems have to be solved to construct the influence matrix. Finally, the modified CSM with domain decomposition, in which the radiative intensity is decomposed into three components, the real wall-related one, the virtual shared interface-related one, and the medium-related one, is proposed. The first two components are solved analytically, and the last one is still solved by the CSM. With such treatments, the computational cost is slightly increased, but the ray effect originated from step-change temperature of medium or step-change optical parameters can be effectively mitigated. Besides, the modified CSM with domain decomposition can also avoid the ray effect due to shadowing singularities. But it should be noted that, in such case, the ray effect due to inhomogeneous spatial distribution of source term may emerge. In conclusion, the CSM combined with domain decomposition is a good alternative method for thermal radiation calculation in complex geometry which can be decomposed into regular subdomains. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
43. 2D Newton Schwarz Legendre Collocation Method for a Convection Problem.
- Author
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Martínez, Darío, Herrero, Henar, and Pla, Francisco
- Subjects
- *
COLLOCATION methods , *NEWTON-Raphson method , *NAVIER-Stokes equations , *HEAT equation , *RAYLEIGH-Benard convection , *DOMAIN decomposition methods , *RAYLEIGH number , *LINEAR equations - Abstract
In this work, an alternate Schwarz domain decomposition method is proposed to solve a Rayleigh–Bénard problem. The problem is modeled with the incompressible Navier–Stokes equations coupled with a heat equation in a rectangular domain. The Boussinesq approximation is considered. The nonlinearity is solved with Newton's method. Each iteration of Newton's method is discretized with an alternating Schwarz scheme, and each Schwarz problem is solved with a Legendre collocation method. The original domain is divided into several subdomains in both directions of the plane. Legendre collocation meshes are coarse, so the problem in each subdomain is well conditioned, and the size of the total mesh can grow by increasing the number of subdomains. In this way, the ill conditioning of Legendre collocation is overcome. The present work achieves an efficient alternating Schwarz algorithm such that the number of subdomains can be increased indefinitely in both directions of the plane. The method has been validated with a benchmark with numerical solutions obtained with other methods and with real experiments. Thanks to this domain decomposition method, the aspect ratio and Rayleigh number can be increased considerably by adding subdomains. Rayleigh values near to the turbulent regime can be reached. Namely, the great advantage of this method is that we obtain solutions close to turbulence, or in domains with large aspect ratios, by solving systems of linear equations with well-conditioned matrices of maximum size one thousand. This is an advantage over other methods that require solving systems with huge matrices of the order of several million, usually with conditioning problems. The computational cost is comparable to other methods, and the code is parallelizable. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
44. Implementation of balancing domain decomposition method for parallel finite element analysis involving inactive elements.
- Author
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Yusa, Yasunori, Kobayashi, Hiroaki, Murakami, Yuma, and Okada, Hiroshi
- Subjects
DOMAIN decomposition methods ,METAL analysis ,TOPOLOGY ,DEGREES of freedom - Abstract
The present study developed a numerical method to implement domain decomposition (DD) solvers with the diagonal‐scaling preconditioner, the balancing domain decomposition (BDD) preconditioner and the BDD with diagonal scaling (BDD‐DIAG) preconditioner, for inactive elements. The inactive element, which is a finite element having zero stiffness, is used in several fields such as multi‐pass welding analysis, additive manufacturing analysis, damage analysis, and topology optimization. For this sort of analysis, we adopted the one‐time decomposition approach, in which the DD process is performed once at the beginning of the analysis. Based on this approach, we formulated the matrix–vector multiplication, the preconditioning and the vector operations in the algorithm of the conjugate gradient method, along with the inactive elements and floating degrees of freedom caused by the inactive elements. Consideration of the inactive elements is enabled by the slight modifications of matrices and vectors in the algorithm. Numerical examples confirmed the scalability of the BDD and BDD‐DIAG preconditioners with the present implementation method. Moreover, the capability of the present method for damage analysis, topology computation, and thermal elastic–plastic analysis of metal additive manufacturing problems was demonstrated. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
45. Balancing Domain Decomposition Method on Additive Schwartz Framework for Multi-Level Implementation
- Author
-
Yamada, Tomonori, Goto, Kazuya, Barth, Timothy J., Series Editor, Griebel, Michael, Series Editor, Keyes, David E., Series Editor, Nieminen, Risto M., Series Editor, Roose, Dirk, Series Editor, Schlick, Tamar, Series Editor, van Brummelen, Harald, editor, Corsini, Alessandro, editor, Perotto, Simona, editor, and Rozza, Gianluigi, editor
- Published
- 2020
- Full Text
- View/download PDF
46. Convergence Study of a DDFV Scheme for the Navier-Stokes Equations Arising in the Domain Decomposition Setting
- Author
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Goudon, Thierry, Krell, Stella, Lissoni, Giulia, Klöfkorn, Robert, editor, Keilegavlen, Eirik, editor, Radu, Florin A., editor, and Fuhrmann, Jürgen, editor
- Published
- 2020
- Full Text
- View/download PDF
47. Optimized Overlapping DDFV Schwarz Algorithms
- Author
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Gander, Martin J., Halpern, Laurence, Hubert, Florence, Krell, Stella, Klöfkorn, Robert, editor, Keilegavlen, Eirik, editor, Radu, Florin A., editor, and Fuhrmann, Jürgen, editor
- Published
- 2020
- Full Text
- View/download PDF
48. Overlapping Schwarz Preconditioner for Fourth Order Multiscale Elliptic Problems
- Author
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Marcinkowski, Leszek, Rahman, Talal, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Woeginger, Gerhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Wyrzykowski, Roman, editor, Deelman, Ewa, editor, Dongarra, Jack, editor, and Karczewski, Konrad, editor
- Published
- 2020
- Full Text
- View/download PDF
49. A parallel scalable domain decomposition preconditioner for elastic crack simulation using XFEM.
- Author
-
Tian, Wei, Huang, Jingjing, Jiang, Yi, and Chen, Rongliang
- Subjects
PARALLEL algorithms ,DOMAIN decomposition methods ,LINEAR equations ,DEGREES of freedom - Abstract
In this article, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the computational mesh into two types of subdomains: the regular subdomains and the crack tip subdomains based on the observation that the crack tips have a significant impact on the convergence of the iterative method while the impact of the crack lines is not that different from those of regular mesh points. The tip subdomains consist of mesh points at crack tips and all neighboring points where the branch enrichment functions are applied. The regular subdomains consist of all other mesh points, including those on the crack lines. To overcome the mismatch between the number of subdomains and the number of processor cores, the proposed method is divided into two steps: solve the crack tip problem and then the regular subdomain problem during each iteration. The proposed method was used to develop a parallel XFEM package which is able to test different types of iterative methods. To achieve good parallel efficiency, additional methods were introduced to reduce communication and to maintain the load balance between processors. Numerical experiments indicate that the proposed method significantly reduces the number of iterations and the total computation time compared to the classical methods. In addition, the method scales up to 8192 processor cores with over 70% parallel efficiency to solve problems with more than 2×108$$ 2\times 1{0}^8 $$ degrees of freedom. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
50. An Efficient Integral Equation Method for Full-Wave Analysis of Inhomogeneous Electromagnetic Surfaces With Connected Conductors.
- Author
-
Gholami, Reza, Naseri, Parinaz, Triverio, Piero, and Hum, Sean Victor
- Subjects
- *
INTEGRAL equations , *UNIT cell , *DOMAIN decomposition methods - Abstract
In this article, a generalized macromodeling approach is presented to simulate complex electromagnetic (EM) surfaces consisting of unit cells with connected conductors. Macromodels of each unit cell are produced by applying the equivalence principle on fictitious surfaces encapsulating them. Unit cells often consist of multiple dielectric layers and conductor traces, featuring multiscale structures. Challenges arise when a current-carrying conductor trace traverses the fictitious surface. Hence, a new method based on half Rao–Wilton–Glisson basis functions is proposed to accurately ensure the continuity of the surface currents and avoid singularities at the intersections. The accuracy of the proposed approach is validated by comparing the results with commercial solvers for different EM surfaces. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
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