Optimization of volume fracturing technology for shallow bow horizontal well in a tight sandstone oil reservoir by Chaoli Gao, Chaoli Gao, Shiqing Cheng, Mingwei Wang, Wen Wu, Zhendong Gao, Song Li, Xuangang Meng

“…To improve the production degree of the g 6 reservoir, the fracture model is established using equivalent conductivity and the multigrid method. The pressure response functions of horizontal wells and volume fracturing horizontal wells are established by using the source function, and the relationship between reservoir permeability and starting pressure gradient in the block is calculated. …”
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A Multilevel Heterogeneous ADMM Algorithm for Elliptic Optimal Control Problems with <i>L</i>¹-Control Cost by Xiaotong Chen, Xiaoliang Song, Zixuan Chen, Lijun Xu

“…Motivated by the efficiency of the multigrid method for solving large-scale problems, we combine the multigrid strategy with the iADMM algorithm. …”
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A local Fourier analysis of additive Vanka relaxation for the Stokes equations by Farrell, P, He, Y, MacLachlan, SP

“…Multigrid methods are popular solution algorithms for many discretized PDEs, either as standalone iterative solvers or as preconditioners, due to their high efficiency. …”

Computational optimization of systems governed by partial differential equations / by Borz, Alfio, Schulz, Volker, 1965-, Society for Industrial and Applied Mathematics

Multiscale Monte Carlo equilibration: Pure Yang-Mills theory by Brower, Richard C., Detmold, William, Orginos, Kostas, Pochinsky, Andrew, Endres, Michael G

“…The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.…”
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Multilevel augmented Lagrangian solvers for overconstrained contact formulations* by Krause Rolf, Weiser Martin

“…Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. …”
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Optimal control of probability density functions of stochastic processes by Mario Annunziato, Alfio Borzì

“…Supported in part by the Austrian Science Fund FWF project F3205‐N18 “Fast Multigrid Methods for Inverse Problems”. First published online: 10 Feb 2011…”
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Aerodynamic reconfiguration and multicriterial optimization of centrifugal compressors – a case study by Valeriu DRAGAN

“…Due to advances of multigrid methods and the improved robustness of structured solvers, CFD can nowadays be part of an optimization loop with artificial neural networks or evolutive algorithms. …”
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TOUTATIS: A radio frequency quadrupole code by Romuald Duperrier

“…It is time based, using multigrids methods and adaptive mesh for a fine description of the forces without being time consuming. …”
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Monolithic multigrid for implicit Runge-Kutta discretizations of incompressible fluid flow by Abu-Labdeh, R, MacLachlan, S, Farrell, PE

“…We present numerical results for the incompressible Stokes, Navier–Stokes, and resistive magnetohydrodynamics equations, in two and three dimensions, confirming that these relaxation schemes lead to robust and scalable monolithic multigrid methods for a challenging range of incompressible fluid-flow models.…”

A Cyclic Multi-Stage Implementation of the Full-Waveform Inversion for the Identification of Anomalies in Dams by Muyiwa Alalade, Ina Reichert, Daniel Köhn, Frank Wuttke, Tom Lahmer

“…To obtain high-resolution “interpretable” images of the damaged regions, we drew inspiration from non-linear full-multigrid methods for inverse problems and applied a new cyclic multi-stage full-waveform inversion (FWI) scheme. …”
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A note on multigrid preconditioning for fractional PDE-constrained optimization problems by Harbir Antil, Andrei Drăgănescu, Kiefer Green

“…In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by a fractional diffusion equation. Multigrid methods within the all-at-once approach to solve the first order optimality Karush–Kuhn–Tucker (KKT) systems are widely popular, but their development have relied on the underlying systems being sparse. …”
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Multilevel acceleration of scattering-source iterations with application to electron transport by Clif Drumm, Wesley Fan

“…Convergence of the low-order solves can be further accelerated by applying off-the-shelf incomplete-factorization or algebraic-multigrid methods. Also available is an algorithm that uses a generalized minimum residual (GMRES) iterative method rather than SI for convergence, using a parallel sweep-based solver to build up a Krylov subspace. …”
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Multigrid Relaxation Methods and the Analysis of Lightness, Shading and Flow by Terzopoulos, Demetri

“…Hence, they converge extremely slowly when confronted by the large representations necessary for low-level vision. Application of multigrid methods can overcome this drawback, as we established in previous work on 3-D surface reconstruction. …”
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A general method for electrochemical simulations .1. Formulation of the strategy for two-dimensional simulations by Alden, J, Compton, R

“…The efficiency of these solvers is compared to "brute force" LU factorization, SIP, and multigrid methods for a typical steady-state channel microband problem.…”

Multilevel optimization for dense motion estimation by Kalmoun, El Mostafa, Saaban, Azizan, Ibrahim, Haslinda, Ramli, Razamin, Omar, Zurni

“…This monograph offers design for fast and reliable technique in the dense motion estimation.This Multilevel Optimization for Dense Motion Estimation work blends both theory and applications to equip reader with an understanding of basic concepts necessary to apply in solving dense motion in a sequence of images.Illustrating well-known variation models for dealing with optical flow estimation, this monograph introduces variation models with applications.A host of variation models are outlines such as Horn-Schunck model, Contrast Invariation Models and Models for Large Displacement.Special attention is also given to multilevel optimization techniques namely multiresolution and multigrid methods to improve the convergence of the global optimum when compared to using only one level resolution in the context of computer vision. …”

Stress Based Model for General Rolling Contact with Surface and Subsurface Survival: Application to Gears with Material Inhomogeneities by Guillermo Enrique Morales-Espejel, Armando Félix-Quiñonez, Hugo Boffy

“…The previously used FFT-based, homogeneous elastic dry contact solver (for the calculation of pressure and subsurface stresses) is now replaced by a previously developed Lamé’s equations solver based on Multigrid methods that can handle bonded inhomogeneities in an elastic media. …”
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Graph coarsening: from scientific computing to machine learning by Chen, Jie, Saad, Yousef, Zhang, Zechen

“…In scientific computing, coarsening plays a central role in algebraic multigrid methods as well as the related class of multilevel incomplete LU factorizations. …”
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An augmented Lagrangian preconditioner for the magnetohydrodynamics equations at high Reynold and coupling numbers by Laakmann, F, Farrell, PE, Mitchell, L

“…Our approach relies on specialized parameter-robust multigrid methods for the hydrodynamic and electromagnetic blocks. …”

Kinetic metallic glass evolution model by Hardin, Thomas J., 1988-

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