Search Results - Two-level and multigrid algorithm*

Multigrid algorithms for hp-version interior penalty discontinuous Galerkin methods on polygonal and polyhedral meshes by Antonietti, P. F., Houston, P., Hu, X., Sarti, M., Verani, M.

“…In this paper we analyze the convergence properties of two-level and W-cycle multigrid solvers for the numerical solution of the linear system of equations arising from hp -version symmetric interior…”
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p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier–Stokes equations by Fidkowski, Krzysztof J., Oliver, Todd A., Lu, James, Darmofal, David L.

“… = 0 discretization of the scalar convection–diffusion equation. Fourier analysis of the two-level p-multigrid algorithm for convection…”
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A Multigrid Solver for PDE-Constrained Optimization with Uncertain Inputs by Ciaramella, Gabriele, Nobile, Fabio, Vanzan, Tommaso

“…In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty…”
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Auxiliary space multigrid method based on additive Schur complement approximation by Kraus, J., Lymbery, M., Margenov, S.

“…‐level preconditioner and the additive Schur complement approximation are derived. The two‐level method is recursively extended to define the auxiliary space multigrid algorithm…”
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A p-multigrid compact gas-kinetic scheme for steady-state acceleration by Ji, Xing, Shyy, Wei, Xu, Kun

“… The p-multigrid strategy is a two-level algorithm. On the high-order level, the CGKS with high-order compact initial reconstruction is used to evolve both cell…”
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Multigrid interpretations of the parareal algorithm leading to an overlapping variant and MGRIT by Gander, Martin J., Kwok, Felix, Zhang, Hui

“… We first review the three main interpretations of the parareal algorithm as a two-level method, a direct one, one based on geometric multigrid and one based on algebraic multigrid…”
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Progress with Multigrid Schemes for Hypersonic Flow Problems by Radespiel, R., Swanson, R.C.

“… Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties…”
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Multigrid transfers for nonsymmetric systems based on Schur complements and Galerkin projections by Wiesner, T. A., Tuminaro, R. S., Wall, W. A., Gee, M. W.

“… This connection demonstrates that the convergence rate of a two‐level model multigrid iteration is completely governed by how well the coarse discretization approximates a Schur complement operator…”
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Two level algorithms for partitioned fluid–structure interaction computations by van Zuijlen, A.H., Bosscher, S., Bijl, H.

“… As a result, the two level method can be easily implemented into existing solvers. Two types of two level algorithms were implemented…”
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On Multigrid Methods for Solving Two-Dimensional Boundary-Value Problems by Gurieva, Y. L., Il’in, V. P., Petukhov, A. V.

“… Two-level iterative algorithms in Krylov subspaces based on approximating the Schur complement obtained by eliminating the edge nodes of the coarse grid are described on the example of two-dimensional rectangular grids…”
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Algebraic multigrid block preconditioning for multi-group radiation diffusion equations by Yue, Xiaoqiang, Zhang, Shulei, Xu, Xiaowen, Shi, Shu, Shi, Weidong

“…\) is the number of energy groups. The preconditioning techniques are based on the monolithic classical algebraic multigrid method, physical-variable based coarsening two-level algorithm and two types of block Schur complement preconditioners…”
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Algebraic multigrid methods by Xu, Jinchao, Zikatanov, Ludmil

“… AMG is often understood as the acronym of ‘algebraic multigrid’, but it can also be understood as ‘abstract multigrid…”
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Comparison of Two-Level Preconditioners Derived from Deflation, Domain Decomposition and Multigrid Methods by Tang, J. M., Nabben, R., Vuik, C., Erlangga, Y. A.

“… In the literature, various two-level PCG methods are known, coming from the fields of deflation, domain decomposition and multigrid…”
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Generalizing reduction‐based algebraic multigrid by Zaman, Tareq, Nytko, Nicolas, Taghibakhshi, Ali, MacLachlan, Scott, Olson, Luke, West, Matthew

“… and other problems, relying on heuristic graph algorithms to achieve their performance. Reduction‐based AMG (AMGr) algorithms attempt to formalize these heuristics by providing two…”
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On “Optimal” h‐independent convergence of Parareal and multigrid‐reduction‐in‐time using Runge‐Kutta time integration by Friedhoff, Stephanie, Southworth, Ben S.

“…Summary Although convergence of the Parareal and multigrid‐reduction‐in‐time (MGRIT) parallel‐in‐time algorithms is well studied, results on their optimality is limited…”
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A multigrid solver for PDE-constrained optimization with uncertain inputs by Ciaramella, Gabriele, Nobile, Fabio, Vanzan, Tommaso

“…In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty…”
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Scalable algorithms for three-field mixed finite element coupled poromechanics by Castelletto, Nicola, White, Joshua A., Ferronato, Massimiliano

“…×3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach…”
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Two-level Schwarz Methods for Hybridizable Discontinuous Galerkin Methods by Lu, Peipei, Rupp, Andreas, Kanschat, Guido

“…In this paper, we propose two-level domain decomposition methods for hybridizable discontinuous Galerkin discretizations including hybridized local discontinuous Galerkin, Raviart–Thomas, and Brezzi–Douglas…”
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A p-multigrid compact gas-kinetic scheme for steady-state acceleration by Ji, Xing, Shyy, Wei, Xu, Kun

“… The p-multigrid strategy is a two-level algorithm. On the high-order level, the high-order CGKS is used to evolve both cell-averaged conservative flow variables…”
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An Extrapolation Cascadic Multigrid Method Combined with a Fourth-Order Compact Scheme for 3D Poisson Equation by Pan, Kejia, He, Dongdong, Hu, Hongling

“…) method with a relative residual stopping criterion. By combining the Richardson extrapolation and tri-quartic Lagrange interpolation for the numerical solutions from two-level of grids…”
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