Relevant bibliographies by topics / Geometric preconditioner

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Academic literature on the topic 'Geometric preconditioner'

Author: Grafiati
Published: 23 November 2024
Last updated: 19 July 2025

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Journal articles on the topic "Geometric preconditioner"

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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
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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
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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 Poiss
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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 precondi
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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 metho
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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).
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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 aux
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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
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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
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Dissertations / Theses on the topic "Geometric preconditioner"

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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
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Book chapters on the topic "Geometric preconditioner"

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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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Nakajima Kengo. "Parallel Multistage Preconditioners by Extended Hierarchical Interface Decomposition for Ill-Conditioned Problems." In Advances in Parallel Computing. IOS Press, 2010. https://doi.org/10.3233/978-1-60750-530-3-99.

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In this work, extended version of “Hierarchical Interface Decomposition (HID)” for parallel preconditioning method has been developed. Extension of overlapped elements between domains and effect of thicker separators were considered. Proposed method has been implemented to finite-element based simulations of linear elasticity problems for simple cubic geometries with heterogeneous distribution of distortion angle of elements. The developed code has been tested on the “T2K Open Supercomputer (T2K/Tokyo)” using up to 512 cores. Extended HID provides more robust and scalable performance than original HID and localized-block-Jacobi-type BILU with extension of overlapped elements.
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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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Conference papers on the topic "Geometric preconditioner"

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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 performan
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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 ML
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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 computati
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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 present
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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 obv
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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 subje
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Reports on the topic "Geometric preconditioner"

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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
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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 g
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