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Artykuły w czasopismach na temat „Geometric preconditioner”

Autor: Grafiati
Data publikacji: 23 listopada 2024
Data aktualizacji: 31 lipca 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

A. Gravvanis, George, and Christos K. Filelis-Papadopoulos. "On the multigrid cycle strategy with approximate inverse smoothing." Engineering Computations 31, no. 1 (2014): 110–22. http://dx.doi.org/10.1108/ec-03-2012-0055.

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Purpose – The purpose of this paper is to propose multigrid methods in conjunction with explicit approximate inverses with various cycles strategies and comparison with the other smoothers. Design/methodology/approach – The main motive for the derivation of the various multigrid schemes lies in the efficiency of the multigrid methods as well as the explicit approximate inverses. The combination of the various multigrid cycles with the explicit approximate inverses as smoothers in conjunction with the dynamic over/under relaxation (DOUR) algorithm results in efficient schemes for solving large
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12

Jakub, Fabian, and Bernhard Mayer. "3-D radiative transfer in large-eddy simulations – experiences coupling the TenStream solver to the UCLA-LES." Geoscientific Model Development 9, no. 4 (2016): 1413–22. http://dx.doi.org/10.5194/gmd-9-1413-2016.

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Abstract. The recently developed 3-D TenStream radiative transfer solver was integrated into the University of California, Los Angeles large-eddy simulation (UCLA-LES) cloud-resolving model. This work documents the overall performance of the TenStream solver as well as the technical challenges of migrating from 1-D schemes to 3-D schemes. In particular the employed Monte Carlo spectral integration needed to be reexamined in conjunction with 3-D radiative transfer. Despite the fact that the spectral sampling has to be performed uniformly over the whole domain, we find that the Monte Carlo spect
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13

Turek, Vojtěch. "Improving Performance of Simplified Computational Fluid Dynamics Models via Symmetric Successive Overrelaxation." Energies 12, no. 12 (2019): 2438. http://dx.doi.org/10.3390/en12122438.

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The ability to model fluid flow and heat transfer in process equipment (e.g., shell-and-tube heat exchangers) is often critical. What is more, many different geometric variants may need to be evaluated during the design process. Although this can be done using detailed computational fluid dynamics (CFD) models, the time needed to evaluate a single variant can easily reach tens of hours on powerful computing hardware. Simplified CFD models providing solutions in much shorter time frames may, therefore, be employed instead. Still, even these models can prove to be too slow or not robust enough w
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14

Roberts, Nathan V. "Camellia: A Rapid Development Framework for Finite Element Solvers." Computational Methods in Applied Mathematics 19, no. 3 (2019): 581–602. http://dx.doi.org/10.1515/cmam-2018-0218.

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AbstractThe discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan guarantees the optimality of the finite element solution in a user-controllable energy norm, and provides several features supporting adaptive schemes. The approach provides stability automatically; there is no need for carefully derived numerical fluxes (as in DG schemes) or for mesh-dependent stabilization terms (as in stabilized methods). In this paper, we focus on features of Camellia that facilitate implementation of new DPG formulations; chief among these is a rich set of features in support of sy
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15

Neymeyr, Klaus. "A Geometric Convergence Theory for the Preconditioned Steepest Descent Iteration." SIAM Journal on Numerical Analysis 50, no. 6 (2012): 3188–207. http://dx.doi.org/10.1137/11084488x.

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16

Knyazev, Andrew V., and Klaus Neymeyr. "Gradient Flow Approach to Geometric Convergence Analysis of Preconditioned Eigensolvers." SIAM Journal on Matrix Analysis and Applications 31, no. 2 (2009): 621–28. http://dx.doi.org/10.1137/080727567.

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17

Neymeyr, Klaus. "A geometric theory for preconditioned inverse iteration applied to a subspace." Mathematics of Computation 71, no. 237 (2001): 197–217. http://dx.doi.org/10.1090/s0025-5718-01-01357-6.

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18

Drmač, Zlatko, and Krešimir Veselić. "Approximate eigenvectors as preconditioner." Linear Algebra and its Applications 309, no. 1-3 (2000): 191–215. http://dx.doi.org/10.1016/s0024-3795(00)00046-x.

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19

Chen, Jian-Long, and Xiao-Qing Jin. "The generalized superoptimal preconditioner." Linear Algebra and its Applications 432, no. 1 (2010): 203–17. http://dx.doi.org/10.1016/j.laa.2009.06.045.

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20

Neymeyr, Klaus. "A geometric theory for preconditioned inverse iteration I: Extrema of the Rayleigh quotient." Linear Algebra and its Applications 322, no. 1-3 (2001): 61–85. http://dx.doi.org/10.1016/s0024-3795(00)00239-1.

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21

Neymeyr, Klaus. "A geometric theory for preconditioned inverse iteration IV: On the fastest convergence cases." Linear Algebra and its Applications 415, no. 1 (2006): 114–39. http://dx.doi.org/10.1016/j.laa.2005.06.022.

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22

Bender, M., and A. Raabe. "Preconditions to ground based GPS water vapour tomography." Annales Geophysicae 25, no. 8 (2007): 1727–34. http://dx.doi.org/10.5194/angeo-25-1727-2007.

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Abstract. The GPS water vapour tomography is a new technique which provides spatially resolved water vapour distributions in the atmosphere under all weather conditions. This work investigates the information contained in a given set of GPS signals as a precondition to an optimal tomographic reconstruction. The spatial distribution of the geometric intersection points between different ray paths is used to estimate the information density. Different distributions of intersection points obtained from hypothetical GPS networks with varying densities of GPS stations are compared with respect to t
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23

Cai, Ming-Chao, and Xiao-Qing Jin. "A note on T. Chan’s preconditioner." Linear Algebra and its Applications 376 (January 2004): 283–90. http://dx.doi.org/10.1016/j.laa.2003.07.005.

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24

Cai, Ming-Chao, Xiao-Qing Jin, and Yi-Min Wei. "A generalization of T. Chan’s preconditioner." Linear Algebra and its Applications 407 (September 2005): 11–18. http://dx.doi.org/10.1016/j.laa.2005.04.014.

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25

Kamatani, K. "Ergodicity of Markov chain Monte Carlo with reversible proposal." Journal of Applied Probability 54, no. 2 (2017): 638–54. http://dx.doi.org/10.1017/jpr.2017.22.

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Abstract We describe the ergodic properties of some Metropolis–Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually analyzed under a subgeometric ergodic framework, but we prove that the mixed preconditioned Crank–Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed target distributions. This useful property comes from the fact that, under a suitable transformation, the MpCN algorithm becomes a random-walk Metropolis algorithm.
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26

Laird, Avery, Bangtian Liu, Nikolaj Bjørner, and Maryam Mehri Dehnavi. "SpEQ: Translation of Sparse Codes using Equivalences." Proceedings of the ACM on Programming Languages 8, PLDI (2024): 1680–703. http://dx.doi.org/10.1145/3656445.

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We present SpEQ, a quick and correct strategy for detecting semantics in sparse codes and enabling automatic translation to high-performance library calls or domain-specific languages (DSLs). When sparse linear algebra codes contain implicit preconditions about how data is stored that hamper direct translation, SpEQ identifies the high-level computation along with storage details and related preconditions. A run-time check guards the translation and ensures that required preconditions are met. We implement SpEQ using the LLVM framework, the Z3 solver, and egglog library and correctly translate
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27

Boman, E., and I. Koltracht. "Computing preconditioners via subspace projection." Linear Algebra and its Applications 302-303 (December 1999): 347–53. http://dx.doi.org/10.1016/s0024-3795(99)00143-3.

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28

Pang, Hong-Kui, Ying-Ying Zhang, Seak-Weng Vong, and Xiao-Qing Jin. "Circulant preconditioners for pricing options." Linear Algebra and its Applications 434, no. 11 (2011): 2325–42. http://dx.doi.org/10.1016/j.laa.2010.03.034.

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Cheng, Che-Man, and Xiao-Qing Jin. "Some stability properties of T. Chan’s preconditioner." Linear Algebra and its Applications 395 (January 2005): 361–65. http://dx.doi.org/10.1016/j.laa.2004.09.010.

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30

Chen, C., and O. Bíró. "Three-dimensional time-harmonic eddy current problems solved by the geometric multigrid preconditioned conjugate gradient method." IET Science, Measurement & Technology 6, no. 5 (2012): 319. http://dx.doi.org/10.1049/iet-smt.2011.0117.

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31

Cho, Durkbin. "Isogeometric Schwarz Preconditioners with Generalized B-Splines for the Biharmonic Problem." Axioms 12, no. 5 (2023): 452. http://dx.doi.org/10.3390/axioms12050452.

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We construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in the ratio between subdomains and overlap sizes. Our analysis is validated through a set of numerical experiments that illustrate good behavior of the proposed preconditioner with respect to the model parameters.
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32

ZOU, QI, XIANG-LIN HUANG, and SI-WEI LUO. "MULTIRESOLUTION IMAGE PERCEPTUAL GROUPING USING TOPOLOGICAL STRUCTURE EMBEDDED IN MANIFOLD." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 01 (2007): 39–49. http://dx.doi.org/10.1142/s0219691307001641.

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Contour grouping is the precondition for high-level visual tasks such as region-of-interest detection and object recognition. Those methods adopting local geometric features and simple photometric attributes always lead to unreliable result or bad robustness. In this paper, we propose a grouping method using multiresolution analysis and one-dimensional manifold. By using multiresolution analysis, grouping seeds and initial clusters are detected as precondition for describing topological structure. Then one-dimensional manifold is applied to discovering intrinsic order of topological structure,
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33

Chan, Raymond H., and Kwok-Po Ng. "Toeplitz preconditioners for Hermitian Toeplitz systems." Linear Algebra and its Applications 190 (September 1993): 181–208. http://dx.doi.org/10.1016/0024-3795(93)90226-e.

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34

Taher, Mardeen Sh, and Salah G. Shareef. "A Combined Conjugate Gradient Quasi-Newton Method with Modification BFGS Formula." International Journal of Analysis and Applications 21 (April 3, 2023): 31. http://dx.doi.org/10.28924/2291-8639-21-2023-31.

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The conjugate gradient and Quasi-Newton methods have advantages and drawbacks, as although quasi-Newton algorithm has more rapid convergence than conjugate gradient, they require more storage compared to conjugate gradient algorithms. In 1976, Buckley designed a method that combines the CG method with QN updates, which is better than that observed for conjugate gradient algorithms but not as good as the quasi-Newton approach. This type of method is called the preconditioned conjugate gradient (PCG) method. In this paper, we introduce two new preconditioned conjugate gradient (PCG) methods that
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35

Hyka (Xhako), Dafina, and Rudina Osmanaj (Zeqirllari). "Fast algorithms for chiral fermions in 2 dimensions." EPJ Web of Conferences 175 (2018): 14005. http://dx.doi.org/10.1051/epjconf/201817514005.

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In lattice QCD simulations the formulation of the theory in lattice should be chiral in order that symmetry breaking happens dynamically from interactions. In order to guarantee this symmetry on the lattice one uses overlap and domain wall fermions. On the other hand high computational cost of lattice QCD simulations with overlap or domain wall fermions remains a major obstacle of research in the field of elementary particles. We have developed the preconditioned GMRESR algorithm as fast inverting algorithm for chiral fermions in U(1) lattice gauge theory. In this algorithm we used the geometr
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36

Lin, Fu-Rong, and De-Cai Zhang. "BTTB preconditioners for BTTB least squares problems." Linear Algebra and its Applications 434, no. 11 (2011): 2285–95. http://dx.doi.org/10.1016/j.laa.2009.10.035.

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37

Neymeyr, Klaus. "On preconditioned eigensolvers and Invert–Lanczos processes." Linear Algebra and its Applications 430, no. 4 (2009): 1039–56. http://dx.doi.org/10.1016/j.laa.2008.10.016.

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38

Jin, Xiao-Qing, and Yi-Min Wei. "A survey and some extensions of T. Chan’s preconditioner." Linear Algebra and its Applications 428, no. 2-3 (2008): 403–12. http://dx.doi.org/10.1016/j.laa.2007.01.021.

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39

Knyazev, Andrew V., and Klaus Neymeyr. "A geometric theory for preconditioned inverse iteration III: A short and sharp convergence estimate for generalized eigenvalue problems." Linear Algebra and its Applications 358, no. 1-3 (2003): 95–114. http://dx.doi.org/10.1016/s0024-3795(01)00461-x.

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Feng, Xiao Mei, Jun Qing Zhan, and Li Shun Li. "Study of the Loading Arms of the Side-Crane Used for Container." Advanced Materials Research 503-504 (April 2012): 896–99. http://dx.doi.org/10.4028/www.scientific.net/amr.503-504.896.

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As the important device, self-loading device plays a key role in the side-crane used for container. And as the key component of the self-loading device, loading arm’s strength analysis is very important. FEA is introduced into the arm’s strength and rigidity analysis, and under the precondition of satisfying allowable stress, minimum weight of the arm is taken as the design target. Ulteriorly, by obtaining optimal geometric parameters, the loading arm’s optimization design can be realized and its manufacture cost can be reduced.
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Ng, Michael K., Raymond H. Chan, Tony F. Chan, and Andy M. Yip. "Cosine transform preconditioners for high resolution image reconstruction." Linear Algebra and its Applications 316, no. 1-3 (2000): 89–104. http://dx.doi.org/10.1016/s0024-3795(99)00274-8.

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Ovtchinnikov, E. "Cluster robustness of preconditioned gradient subspace iteration eigensolvers." Linear Algebra and its Applications 415, no. 1 (2006): 140–66. http://dx.doi.org/10.1016/j.laa.2005.06.039.

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43

Guan, Jianbo, Yu Li, and Guohua Liu. "Preconditioned Conjugate Gradient Algorithm-Based 2D Waveform Inversion for Shallow-Surface Site Characterization." Shock and Vibration 2021 (December 21, 2021): 1–16. http://dx.doi.org/10.1155/2021/3164358.

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The full-waveform inversion (FWI) of a Love wave has become a powerful tool for shallow-surface site characterization. In classic conjugate gradient algorithm- (CG) based FWI, the energy distribution of the gradient calculated with the adjoint state method does not scale with increasing depth, resulting in diminished illumination capability and insufficient model updating. The inverse Hessian matrix (HM) can be used as a preprocessing operator to balance, filter, and regularize the gradient to strengthen the model illumination capabilities at depth and improve the inversion accuracy. However,
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44

Rafiei, A. "Left-looking version of AINV preconditioner with complete pivoting strategy." Linear Algebra and its Applications 445 (March 2014): 103–26. http://dx.doi.org/10.1016/j.laa.2013.11.046.

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MANDAL, J. C., and J. BALLMANN. "UNSTEADY FLOW COMPUTATIONS OVER MOVING BODY USING DYNAMIC MESHES." International Journal of Computational Methods 01, no. 03 (2004): 507–18. http://dx.doi.org/10.1142/s0219876204000253.

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An efficient implicit unstructured grid algorithm for solving unsteady inviscid compressible flows over moving body employing an Arbitrary Lagrangian Eulerian formulation is presented. In the present formulation, the time discretization is performed using a second-order accurate 3-point time integration scheme and the upwind-biased space discretization using second-order accurate finite volume formulation with Venkatakrishnan limiter. The face-velocities of the control volumes are computed using Geometric Conservation Laws. The nonlinear system arising from the implicit formulation is solved u
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Гурьева, Я. Л., В. П. Ильин, and Д. В. Перевозкин. "Algebraic-geometric and information structures of domain decomposition methods." Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), no. 2 (May 26, 2016): 132–46. http://dx.doi.org/10.26089/nummet.v17r213.

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Рассматриваются алгебраические, геометрические и информационные аспекты параллельных методов декомпозиции для решения больших систем линейных уравнений с разреженными матрицами, возникающими при аппроксимации многомерных краевых задач на неструктурированных сетках. Алгоритмы базируются на разбиении сеточной расчетной области на подобласти с параметризованной величиной пересечений и различными интерфейсными условиями на смежных границах. Рассматриваются вопросы, возникающие при алгебраической декомпозиции исходной матрицы. Применяются различные двухуровневые итерационные процессы, включающие в
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Jiao, Niangang, Feng Wang, Hongjian You, Xiaolan Qiu, and Mudan Yang. "Geo-Positioning Accuracy Improvement of Multi-Mode GF-3 Satellite SAR Imagery Based on Error Sources Analysis." Sensors 18, no. 7 (2018): 2333. http://dx.doi.org/10.3390/s18072333.

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The GaoFen-3 (GF-3) satellite is the only synthetic aperture radar (SAR) satellite in the High-Resolution Earth Observation System Project, which is the first C-band full-polarization SAR satellite in China. In this paper, we proposed some error sources-based weight strategies to improve the geometric performance of multi-mode GF-3 satellite SAR images without using ground control points (GCPs). To get enough tie points, a robust SAR image registration method and the SAR-features from accelerated segment test (SAR-FAST) method is used to achieve the image registration and tie point extraction.
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Wu, Yanze, and Joseph E. Subotnik. "A quantum-classical Liouville formalism in a preconditioned basis and its connection with phase-space surface hopping." Journal of Chemical Physics 158, no. 2 (2023): 024115. http://dx.doi.org/10.1063/5.0124835.

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We revisit a recent proposal to model nonadiabatic problems with a complex-valued Hamiltonian through a phase-space surface hopping (PSSH) algorithm employing a pseudo-diabatic basis. Here, we show that such a pseudo-diabatic PSSH (PD-PSSH) ansatz is consistent with a quantum-classical Liouville equation (QCLE) that can be derived following a preconditioning process, and we demonstrate that a proper PD-PSSH algorithm is able to capture some geometric magnetic effects (whereas the standard fewest switches surface hopping approach cannot capture such effects). We also find that a preconditioned
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Jbilou, K. "ADI preconditioned Krylov methods for large Lyapunov matrix equations." Linear Algebra and its Applications 432, no. 10 (2010): 2473–85. http://dx.doi.org/10.1016/j.laa.2009.12.025.

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Vecharynski, Eugene, and Andrew Knyazev. "Preconditioned steepest descent-like methods for symmetric indefinite systems." Linear Algebra and its Applications 511 (December 2016): 274–95. http://dx.doi.org/10.1016/j.laa.2016.09.011.

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