Thematische Bibliographien / Geometric preconditioner

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Auswahl der wissenschaftlichen Literatur zum Thema „Geometric preconditioner“

Autor: Grafiati

Veröffentlicht am 23. November 2024

Zuletzt aktualisiert am 7. Juli 2025

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Zeitschriftenartikel zum Thema "Geometric preconditioner"

Sun, Qingtao, Runren Zhang, Ke Chen, Naixing Feng, and Yunyun Hu. "Anisotropic modeling with geometric multigrid preconditioned finite-element method." GEOPHYSICS 87, no. 3 (2022): A33—A36. http://dx.doi.org/10.1190/geo2021-0592.1.

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Formation anisotropy in complicated geophysical environments can have a significant impact on data interpretation of electromagnetic surveys. To facilitate full 3D modeling of arbitrary anisotropy, we have adopted an [Formula: see text]-version geometric multigrid preconditioned finite-element method (FEM) based on vector basis functions. By using a structured mesh, instead of an unstructured one, our method can conveniently construct the restriction and prolongation operators for multigrid implementation, and then recursively coarsen the grid with the F-cycle coarsening scheme. The geometric multigrid method is used as a preconditioner for the biconjugate-gradient stabilized method to efficiently solve the linear system resulting from the FEM. Our method avoids the need of interpolation for arbitrary anisotropy modeling as in Yee’s grid-based finite-difference method, and it is also more capable of large-scale modeling with respect to the [Formula: see text]-version geometric multigrid preconditioned finite-element method. A numerical example in geophysical well logging is included to demonstrate its numerical performance. Our [Formula: see text]-version geometric multigrid preconditioned FEM is expected to help formation anisotropy characterization with electromagnetic surveys in complicated geophysical environments.

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Cots, Olivier, Rémy Dutto, Sophie Jan, and Serge Laporte. "Geometric preconditioner for indirect shooting and application to hybrid vehicle." IFAC-PapersOnLine 58, no. 21 (2024): 43–48. http://dx.doi.org/10.1016/j.ifacol.2024.10.140.

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Pan, Guangdong, and Aria Abubakar. "Iterative solution of 3D acoustic wave equation with perfectly matched layer boundary condition and multigrid preconditioner." GEOPHYSICS 78, no. 5 (2013): T133—T140. http://dx.doi.org/10.1190/geo2012-0287.1.

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We tested a biconjugate gradient stabilized (BiCGSTAB) solver using a multigrid-based preconditioner for solving the acoustic wave (Helmholtz) equation in the frequency domain. The perfectly matched layer (PML) method was used as the radiation boundary condition (RBC). The equation was discretized using either a second- or fourth-order finite-difference (FD) scheme. The convergence of an iterative solver depended strongly on the RBC used because the spectrum of the discretized equation also depends on it. We used a geometric multigrid approach to construct a preconditioner for our FD frequency-domain (FDFD) forward solver equipped with the PML boundary condition. For efficiency, this preconditioner was only constructed using a second-order FD scheme with negligible attenuation inside the PML domain. The preconditioner was used for accelerating the convergence rate of the FDFD forward solver for cases when the discretization grids were oversampled (i.e., when the number of discretization points per minimum wavelength was greater than 10). The number of multigrid levels was also chosen adaptively depending on the number of discretization grids. We found that the multigrid preconditioner can speed up the total computational time of the BiCGSTAB solver for oversampled cases or at low frequencies. We also observed that the BiCGSTAB solver using an accurate PML boundary condition converged for realistic SEG benchmark models at high frequencies.

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Cai, Mingchao, Andy Nonaka, John B. Bell, Boyce E. Griffith, and Aleksandar Donev. "Efficient Variable-Coefficient Finite-Volume Stokes Solvers." Communications in Computational Physics 16, no. 5 (2014): 1263–97. http://dx.doi.org/10.4208/cicp.070114.170614a.

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AbstractWe investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the success of using the classical projection method as a preconditioner for the coupled velocity pressure system [B. E. Griffith, J. Comp. Phys., 228 (2009), pp. 7565-7595], as well; established techniques for steady and unsteady Stokes flow in the finite-element literature, we construct preconditioners that employ independent generalized Helmholtz and Poisson solvers for the velocity and pressure subproblems. We demonstrate that only a single cycle of a standard geometric multigrid algorithm serves as an effective inexact solver for each of these subproblems. Contrary to traditional wisdom, we find that the Stokes problem can be solved nearly as efficiently as the independent pressure and velocity subproblems, making the overall cost of solving the Stokes system comparable to the cost of classical projection or fractional step methods for incompressible flow, even for steady flow and in the presence of large density and viscosity contrasts. Two of the five preconditioners considered here are found to be robust to GMRES restarts and to increasing problem size, making them suitable for large-scale problems. Our work opens many possibilities for constructing novel unsplit temporal integrators for finite-volume spatial discretizations of the equations of low Mach and incompressible flow dynamics.

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de Prenter, F., C. V. Verhoosel, E. H. van Brummelen, et al. "Multigrid solvers for immersed finite element methods and immersed isogeometric analysis." Computational Mechanics 65, no. 3 (2019): 807–38. http://dx.doi.org/10.1007/s00466-019-01796-y.

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AbstractIll-conditioning of the system matrix is a well-known complication in immersed finite element methods and trimmed isogeometric analysis. Elements with small intersections with the physical domain yield problematic eigenvalues in the system matrix, which generally degrades efficiency and robustness of iterative solvers. In this contribution we investigate the spectral properties of immersed finite element systems treated by Schwarz-type methods, to establish the suitability of these as smoothers in a multigrid method. Based on this investigation we develop a geometric multigrid preconditioner for immersed finite element methods, which provides mesh-independent and cut-element-independent convergence rates. This preconditioning technique is applicable to higher-order discretizations, and enables solving large-scale immersed systems at a computational cost that scales linearly with the number of degrees of freedom. The performance of the preconditioner is demonstrated for conventional Lagrange basis functions and for isogeometric discretizations with both uniform B-splines and locally refined approximations based on truncated hierarchical B-splines.

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Yuan, Yu-Xin, A.-Man Li, Ting Hu, and Hong Liu. "An anisotropic multilevel preconditioner for solving the Helmholtz equation with unequal directional sampling intervals." GEOPHYSICS 85, no. 6 (2020): T293—T300. http://dx.doi.org/10.1190/geo2019-0330.1.

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An efficient finite-difference method for solving the isotropic Helmholtz equation relies on a discretization scheme and an appropriate solver. Accordingly, we have adopted an average-derivative optimal scheme that has two advantages: (1) it can be applied to unequal directional sampling intervals and (2) it requires less than four grid points of sampling per wavelength. Direct methods are not of interest for industry-sized problems due to the high memory requirements; Krylov subspace methods such as the biconjugate gradient stabilized method and the flexible generalized minimal residual method that combine a multigrid-based preconditioner are better alternatives. However, standard geometric multigrid algorithms fail to converge when there exist unequal directional sampling intervals; this is called anisotropic grids in terms of the multigrid. We first review our previous research on 2D anisotropic grids: the semicoarsening strategy, line-wise relaxation operator, and matrix-dependent interpolation were used to modify the standard V-cycle multigrid algorithms, resulting in convergence. Although directly extending to the 3D case by substituting line relaxation for plane relaxation deteriorates the convergence rate considerably, we then find that a multilevel generalized minimal residual preconditioner-combined semicoarsening strategy is more suitable for anisotropic grids and the convergence rate is faster in the 2D and 3D cases. The results of the numerical experiments indicate that the standard geometric multigrid does not work for anisotropic grids, whereas our method demonstrates a faster convergence rate than the previous method.

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FENG, QUANDONG, JINGFANG HUANG, NINGMING NIE, ZAIJIU SHANG, and YIFA TANG. "IMPLEMENTING ARBITRARILY HIGH-ORDER SYMPLECTIC METHODS VIA KRYLOV DEFERRED CORRECTION TECHNIQUE." International Journal of Modeling, Simulation, and Scientific Computing 01, no. 02 (2010): 277–301. http://dx.doi.org/10.1142/s1793962310000171.

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In this paper, an efficient numerical procedure is presented to implement the Gaussian Runge–Kutta (GRK) methods (also called Gauss methods). The GRK technique first discretizes each marching step of the initial value problem using collocation formulations based on Gaussian quadrature. As is well known, it preserves the geometric structures of Hamiltonian systems. Existing analysis shows that the GRK discretization with s nodes is of order 2s, A-stable, B-stable, symplectic and symmetric, and hence "optimal" for solving initial value problems of general ordinary differential equations (ODEs). However, as the unknowns at different collocation points are coupled in the discretized system, direct solution of the resulting algebraic equations is in general inefficient. Instead, we use the Krylov deferred correction (KDC) method in which the spectral deferred correction (SDC) scheme is applied as a preconditioner to decouple the original system, and the resulting preconditioned nonlinear system is solved efficiently using Newton–Krylov schemes such as Newton–GMRES method. The KDC accelerated GRK methods have been applied to several Hamiltonian systems and preliminary numerical results are presented to show the accuracy, stability, and efficiency features of these methods for different accuracy requirements in short- and long-time simulations.

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Martynenko, S. I. "Potentialities of the Robust Multigrid Technique." Computational Methods in Applied Mathematics 10, no. 1 (2010): 87–94. http://dx.doi.org/10.2478/cmam-2010-0004.

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AbstractThe present paper discusses the parallelization of the robust multigrid technique (RMT) and the possible way of applying this to unstructured grids. As opposed to the classical multigrid methods, the RMT is a trivial method of parallelization on coarse grids independent of the smoothing iterations. Estimates of the minimum speed-up and parallelism efficiency are given. An almost perfect load balance is demonstrated in a 3D illustrative test. To overcome the geometric nature of the technique, the RMT is used as a preconditioner in solving PDEs on unstructured grids. The procedure of auxiliary structured grids generation is considered in details.

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Nammour, Rami, and William W. Symes. "Multiparameter Inversion: Cramer's Rule for Pseudodifferential Operators." International Journal of Geophysics 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/780291.

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Linearized multiparameter inversion is a model-driven variant of amplitude-versus-offset analysis, which seeks to separately account for the influences of several model parameters on the seismic response. Previous approaches to this class of problems have included geometric optics-based (Kirchhoff, GRT) inversion and iterative methods suitable for large linear systems. In this paper, we suggest an approach based on the mathematical nature of the normal operator of linearized inversion—it is a scaling operator in phase space—and on a very old idea from linear algebra, namely, Cramer's rule for computing the inverse of a matrix. The approximate solution of the linearized multiparameter problem so produced involves no ray theory computations. It may be sufficiently accurate for some purposes; for others, it can serve as a preconditioner to enhance the convergence of standard iterative methods.

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Chen, Shu-Wen, Feng Lu, and Yao Ma. "Fitting Green’s Function FFT Acceleration Applied to Anisotropic Dielectric Scattering Problems." International Journal of Antennas and Propagation 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/123739.

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A volume integral equation based fast algorithm using the Fast Fourier Transform of fitting Green’s function (FG-FFT) is proposed in this paper for analysis of electromagnetic scattering from 3D anisotropic dielectric objects. For the anisotropic VIE model, geometric discretization is still implemented by tetrahedron cells and the Schaubert-Wilton-Glisson (SWG) basis functions are also used to represent the electric flux density vectors. Compared with other Fast Fourier Transform based fast methods, using fitting Green’s function technique has higher accuracy and can be applied to a relatively coarse grid, so the Fast Fourier Transform of fitting Green’s function is selected to accelerate anisotropic dielectric model of volume integral equation for solving electromagnetic scattering problems. Besides, the near-field matrix elements in this method are used to construct preconditioner, which has been proved to be effective. At last, several representative numerical experiments proved the validity and efficiency of the proposed method.

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Dissertationen zum Thema "Geometric preconditioner"

Dutto, Rémy. "Méthode à deux niveaux et préconditionnement géométrique en contrôle optimal. Application au problème de répartition de couple des véhicules hybrides électriques." Electronic Thesis or Diss., Université de Toulouse (2023-....), 2024. http://www.theses.fr/2024TLSEP088.

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Motivé par le problème industriel de répartition de couple dans les véhicules hybrides électriques, ce travail propose principalement deux nouvelles méthodes de résolution indirectes de problèmes de commande optimale. La première est la méthode Macro-Micro qui est basée sur une décomposition à deux niveaux du problème de commande optimale, faisant intervenir les fonctions valeur de Bellman de manière explicite à des temps préalablement fixés. Ces fonctions sont connues pour être assez difficile à construire. L’idée principale est d’approcher ces fonctions valeur par des réseaux de neurones, ce qui mène à une résolution hiérarchique d’un problème d’optimisation en dimension faible et d’un ensemble de problèmes de commande optimale définis sur des intervalles de temps plus courts. La seconde est une méthode de préconditionnement géométrique qui permet une résolution plus efficace du problème de commande optimale. Cette méthode, basée sur l’interprétation géométrique du co-état et sur la transformée de Mathieu, utilise un changement de variable linéaire à partir de la simple transformation d’une ellipse en cercle. Ces deux méthodes, bien que présentées séparément, peuvent être combinées et mènent à une résolution plus rapide, robuste et légère du problème de répartition de couple, permettant ainsi que de s’approcher des critères d’embarquabilités<br>Motivated by the torque split and gear shift industrial problem of hybrid electric vehicles, this work mainly proposes two new indirect optimal control problem methods. The first one is the Macro-Micro method, which is based on a bilevel decomposition of the optimal control problem and uses Bellman’s value functions at fixed times. These functions are known to be difficult to create. The main idea of this method is to approximate these functions by neural networks, which leads to a hierarchical resolution of a low dimensional optimization problem and a set of independent optimal control problems defined on smaller time intervals. The second one is a geometric preconditioning method, which allows a more efficient resolution of the optimal control problem. This method is based on a geometrical interpretation of the Pontryagin’s co-state and on the Mathieu transformation, and uses a linear diffeomorphism which transforms an ellipse into a circle. These two methods, presented separately, can be combined and lead together to a fast, robust and light resolution for the torque split and gear shift optimal control problem, closer to the embedded requirements

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Buchteile zum Thema "Geometric preconditioner"

Olas, Tomasz. "Parallel Geometric Multigrid Preconditioner for 3D FEM in NuscaS Software Package." In Parallel Processing and Applied Mathematics. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-55224-3_17.

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Calandra, H., S. Gratton, and X. Vasseur. "A Geometric Multigrid Preconditioner for the Solution of the Helmholtz Equation in Three-Dimensional Heterogeneous Media on Massively Parallel Computers." In Modern Solvers for Helmholtz Problems. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-28832-1_6.

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Campos, Fernando Otaviano, Rafael Sachetto Oliveira, and Rodrigo Weber dos Santos. "Performance Comparison of Parallel Geometric and Algebraic Multigrid Preconditioners for the Bidomain Equations." In Computational Science – ICCS 2006. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11758501_15.

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Christiansen, Lasse Hjuler, and John Bagterp Jørgensen. "New Preconditioners for Semi-linear PDE-Constrained Optimal Control in Annular Geometries." In Lecture Notes in Computational Science and Engineering. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-39647-3_35.

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Langer, U., and D. Pusch. "Comparison of Geometrical and Algebraic Multigrid Preconditioners for Data-Sparse Boundary Element Matrices." In Large-Scale Scientific Computing. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11666806_13.

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"A Geometric Toolbox for Tetrahedral Finite Element Partitions." In Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations, edited by Jan Brandts, Sergey Korotov, and Michal Krizek. BENTHAM SCIENCE PUBLISHERS, 2012. http://dx.doi.org/10.2174/978160805291211101010103.

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Carpentieri, Bruno. "Krylov Subspace Methods for Big Data Analysis of Large Computational Electromagnetics Applications." In Frontiers in Artificial Intelligence and Applications. IOS Press, 2021. http://dx.doi.org/10.3233/faia210232.

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In this paper we present some computational techniques based on the class of preconditioned Krylov subspace methods that enable us to carry out large-scale, big data simulations of Computational Electromagnetics applications modeled using integral equations. This analysis requires the solution of large linear systems that cannot be afforded by conventional direct methods (based on variants of the Gaussian elimination algorithm) due to their high memory costs. We show that, thanks to the development of efficient Krylov methods and suitable preconditioning techniques, nowadays the solution of realistic electromagnetic problems that involve tens of million (and sometimes even more) unknowns, has become feasible. However, the choice of the best class of methods for the selected computer hardware and the given geometry remains an open problem that requires further analysis.

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Ventre, Salvatore, Bruno Carpentieri, Gaspare Giovinco, Antonello Tamburrino, Fabio Villone, and Guglielmo Rubinacci. "An Effective H²-LU Preconditioner for Iterative Solution of MQS Integral-Based Formulation P." In Advances in Fusion Energy Research. From Theory to Models, Algorithms, and Applications [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.108106.

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We present iterative solution strategies for solving efficiently Magneto-Quasi-Static (MQS) problems expressed in terms of an integral formulation based on the electric vector potential. Integral formulations give rise to discrete models characterized by linear systems with dense coefficient matrices. Iterative Krylov subspace methods combined with fast compression techniques for the matrix-vector product operation are the only viable approach for treating large scale problems, such as those considered in this study. We propose a fully algebraic preconditioning technique built upon the theory of H2-matrix representation that can be applied to different integral operators and to changes in the geometry, only by tuning a few parameters. Numerical experiments show that the proposed methodology performs much better than the existing one in terms of ability to reduce the number of iterations of a Krylov subspace method, especially for fast transient analysis.

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Konferenzberichte zum Thema "Geometric preconditioner"

Singh, Krishna M., Eldad J. Avital, John J. R. Williams, C. Ji, and A. Munjiza. "Parallel Pressure Poisson Solvers for LES of Complex Geometry Flows." In ASME/JSME/KSME 2015 Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/ajkfluids2015-29748.

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This paper presents an assessment of performance of parallel pre-conditioners for BICGSTAB solver for numerical solution of the pressure Poisson equation arising in large eddy simulation of turbulent incompressible flows. We explore the performance of geometric multigrid pre-conditioner for the non-uniform grid and compare its performance with additive Schwarz pre-conditioner, Jacobi and SOR(k) pre-conditioners. Numerical experiments have been performed for a wide range of non-uniformity (stretching) of the grid. The fictitious domain geometric multigrid preconditioner shows the best performance followed by the SOR(k) preconditioner.

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Singh, Abhishek Kumar, and Krishna Mohan Singh. "GMRES Solver for MLPG Method Applied to Heat Conduction." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-24566.

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Abstract In recent years, meshless local Petrov-Galerkin (MLPG) method has emerged as the promising choice for solving variety of scientific and engineering problems. MLPG formulation leads to a non-symmetric system of algebraic equations. Iterative methods (such as GMRES and BiCGSTAB methods) are more competent than the direct solvers for solving a general linear system of larger size (order of millions or billions). This paper presents the use of GMRES solver with MLPG method for the very first time. The restarted version of the GMRES method is applied in connection with the interpolating MLPG method, to solve steady-state heat conduction in three-dimensional regular geometry. The performance of GMRES solver (with and without preconditioner) has been compared with the preconditioned BiCGSTAB method in terms of computation time and convergence behaviour. Jacobi and successive over-relaxation methods have been used as preconditioners in both the solvers. The results show that GMRES solver takes about 18 to 20% less CPU time than the BiCGSTAB solver along with better convergence behaviour.

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Carrington, David B., and Vincent A. Mousseau. "Preconditioning and Solver Optimization Ideas for Radiative Transfer." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72040.

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In this paper, radiative transfer and time-dependent transport of radiation energy in participating media are modeled using a first-order spherical harmonics method (P1) and radiation diffusion. Partial differential equations for P1 and radiation diffusion are discretized by a variational form of the equations using support operators. Choices made in the discretization result in a symmetric positive definite (SPD) system of linear equations. Modeling multidimensional domains with complex geometries requires a very large system of linear equations with 10s of millions of elements. The computational domain is decomposed into a large number of subdomains that are solved on separate processors resulting in a massively parallel application. The linear system of equations is solved with a preconditioned conjugate gradient method. Various preconditioning techniques are compared in this study. Simple preconditioning techniques include: diagonal scaling, Symmetric Successive Over Relaxation (SSOR), and block Jacobi with SSOR as the block solver. Also, a two-grid multigrid-V-cycle method with aggressive coarsening is explored for use in the problems presented. Results show that depending on the test problem, simple preconditioners are effective, but the more complicated preconditioners such as an algebraic multigrid or the geometric multigrid are most efficient, particularly for larger problems and longer simulations. Optimal preconditioning varies depending on the problem and on how the physical processes evolve in time. For the insitu preconditioning techniques—SSOR and block Jacobi—a fuzzy controller can determine the optimal reconditioning process. Discussions of the current knowledge-based controller, an optimization search algorithm, are presented. Discussions of how this search algorithm can be incorporated into the development of data-driven controller incorporating clustering and subsequent construction of the fuzzy model from partitions are also discussed.

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Udaykumar, H. S., R. Mittal, and W. Shyy. "Simulation of Flow and Heat Transfer With Phase Boundaries and Complex Geometries on Cartesian Grids." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-1093.

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Abstract This paper is an extension of our previous work on simulation of complex phase front evolution in the diffusion-dominated situation. The Navier-Stokes equations are solved using a finite-volume method based on a second-order accurate central-difference scheme in conjunction with a two-step fractional-step procedure. The key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries. A new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second-order spatial accuracy of the underlying solver. The presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations. The convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh. The accuracy and fidelity of the solver is validated and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated. The method will be useful in studying the effects of fluid flow on the evolution of complex solid-liquid phase boundaries.

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Kang, Suhyun, Duhun Hwang, Moonjung Eo, Taesup Kim, and Wonjong Rhee. "Meta-Learning with a Geometry-Adaptive Preconditioner." In 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2023. http://dx.doi.org/10.1109/cvpr52729.2023.01543.

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Stroia, Iulian, Lucian Itu, Cosmin Nita, Laszlo Lazar, and Constantin Suciu. "GPU accelerated geometric multigrid method: Comparison with preconditioned conjugate gradient." In 2015 IEEE High Performance Extreme Computing Conference (HPEC). IEEE, 2015. http://dx.doi.org/10.1109/hpec.2015.7322480.

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Chao Chen and O. Biro. "3-D time-harmonic Eddy current problems solved by the geometric multigrid preconditioned conjugate gradient method." In IET 8th International Conference on Computation in Electromagnetics (CEM 2011). IET, 2011. http://dx.doi.org/10.1049/cp.2011.0017.

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Adrian, Simon B., Francesco P. Andriullil, and Thomas F. Eibert. "A Refinement - Free Calderón Preconditioner for the Electric Field Integral Equation on Geometries with Junctions." In 2018 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting. IEEE, 2018. http://dx.doi.org/10.1109/apusncursinrsm.2018.8609072.

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Larsen, Lance C. "Identifying the Cause of and Fixing Ill-Conditioned Matrices in Nuclear Analysis Codes." In 2020 International Conference on Nuclear Engineering collocated with the ASME 2020 Power Conference. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/icone2020-16903.

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Abstract Many of the analytical codes used in the nuclear industry, such as TRACE, RELAP5, and PARCS, approximate the equations that model the physics via a linearized system of equations. One common difficulty when solving linearized systems is that an accurately formulated system of equations may be ill-conditioned. Ill-conditioned matrices can result in significant amplification of error leading to poor, or even invalid, results. Ill-conditioned matrices lead to some challenging issues for the analytical code developers: • An ill-conditioned matrix is often solvable, and there may be no obvious indication numerically that something has gone wrong even though numerical error is large. Thus, how can ill-conditioning be effectively detected for a matrix? • When ill-conditioning is detected, how can the source of the ill-conditioning be determined so that it can be analyzed and corrected? Ill-conditioning is fundamentally a geometric problem that can be understood with geometric concepts associated with matrices and vectors. Geometric concepts and tools, useful for understanding the cause of ill-conditioning of a matrix, are presented. A geometric understanding of ill-conditioning can point to the rows or columns of the matrix that most contribute to ill-conditioning so that the source of ill-conditioning can be analyzed and understood, and leads to techniques for building matrix preconditioners to improve the solvability of the matrix.

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Jakupi, Pellumb, Bill Santos, Wilfred Binns, Ivan Barker, and Jenny Been. "Microstructural Feature Analysis of X65 Steel Exposed to Ripple Load Testing Under Near Neutral pH Conditions." In 2014 10th International Pipeline Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/ipc2014-33230.

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Newly designed miniature Compact Tension (CT) specimens, designed according to standard ASTM dimension ratios, and machined out of previously in-service X65 pipeline steel were exposed to super-imposed cyclic loading at high mean stresses in NS4 solution to determine the behaviour of X65 steel to ripple loading under near neutral pH conditions. Electron Back-Scatter Diffraction (EBSD) was used to study the microstructural grain geometry to determine if it influences stress-corrosion cracking (SCC) initiation and propagation. Prior to ripple load testing, finely polished X65 surfaces were subjected to EBSD measurements to characterize the microstructure’s geometry; i.e., grain and grain boundary orientations and texture. On the same locations where EBSD maps were recorded, a grid of cross-shaped resist markings — approximately 1–5 μm in size — were deposited every 15 μm across the analyzed surfaces. Following microscopic analyses the specimens were pre-cracked and re-examined to determine whether the crack initiation procedure preconditions the residual strain (quantified by grain misorientations) around an induced crack. Then, ripple load testing at stress levels characterized by load ratios (R) greater than 0.9 was performed, while simultaneously monitoring the open-circuit potential (OCP) at room temperature. The originally characterized surface was again re-examined to determine if the crack tip propagated preferably along a specific crystallographic grain orientation by comparing the shifts in each cross-shaped grid. Results from this investigation will help determine if there is a link between microstructural grain geometries and transgranular stress corrosion cracking.

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Berichte der Organisationen zum Thema "Geometric preconditioner"

Badia, S., A. Martín, J. Principe, C. Soriano, and R. Rossi. D3.1 Report on nonlinear domain decomposition preconditioners and release of the solvers. Scipedia, 2021. http://dx.doi.org/10.23967/exaqute.2021.2.021.

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This document describes the industrial application, on which the developments of the project are implemented, and the CFD set-up. The developments are implemented over six analysis cases with increasing complexity starting from a 2D geometry with mean wind inflow to a 3D geometry with turbulent inflow and real-time shape optimization. The application represents the CAARC tall building model, which has served as a benchmark model for many studies since the 1970’s when it was first developed. Base moments (bending and torsional moments) of the building are extracted for validation by comparison of the results with the benchmark study. Page 3 of 19 Deliverable 7.1

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Kalashnikova, Irina. Preconditioner and convergence study for the Quantum Computer Aided Design (QCAD) nonlinear poisson problem posed on the Ottawa Flat 270 design geometry. Office of Scientific and Technical Information (OSTI), 2012. http://dx.doi.org/10.2172/1044970.

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Brosnahan and DeVries. PR-317-10702-R01 Testing for the Dilation Strength of Salt. Pipeline Research Council International, Inc. (PRCI), 2011. http://dx.doi.org/10.55274/r0010026.

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A laboratory testing program on rock salt specimens was performed using test conditions that are consistent with the stresses that are experienced near the surfaces of salt caverns during storage operation. The proposed work effort focuses on improving the methodology for defining the onset of dilation for rock salt. Geomechanical studies use dilation criteria to assess the potential for salt damage that can lead to spalling in the cavern roof and/or walls and subsequent damage to the cavern or hanging string. This constraint is often the one that limits the minimum gas pressure in a natural gas storage cavern. This report documents the PRCI funded follow-on activities to the recently completed Gas Storage Technology Consortium project [DeVries, 2010]. The work activities completed include the following: Laboratory dilation strength testing of eight specimens having preconditioning durations longer than 10 days. Numerical modeling to identify and optimize an appropriate specimen shape for dilation testing in triaxial extension states of stress. Laboratory constant mean stress extension testing on the optimized specimen shape. DeVries [2010] documented the effects of the preconditioning durations on the dilation strength of salt specimens. Preconditioning of specimens is the process whereby specimens are subject to a relatively high hydrostatic stress for a specified period of time. It is believed that preconditioning mitigates some of the damage to the specimens induced by coring, transporting, and specimen preparation. The study documented by DeVries [2010] suggests that increasing the preconditioning duration increases the dilation strength of salt, with the maximum precondition duration limited to 10 days. This project expands upon these findings through additional testing to determine if preconditioning durations longer than 10 days has any additional benefit. In addition to the preconditioning task, this study will also investigate the variability issues observed during dilation strength tests performed under triaxial extension states of stress. It is hypothesized that the high variability seen in extensional test results might be attributed to end effects caused by (1) the friction at the specimen-platen interface and (2) specimens breaking outside the range measured by gages. To help reduce frictional effects and breakage location issues, numerical models of alternate specimen shapes were created to provide a basis for testing a new specimen geometry. Laboratory tests were performed on the new specimen geometry to validate any of its possible benefits.

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