Searched for: subject%3A%22multigrid%22
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Wiersma, R.T. (author), Nasikun, A. (author), Eisemann, E. (author), Hildebrandt, K.A. (author)
We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid hierarchy to achieve a fast hierarchy construction and to extend the applicability of the method from triangle...
conference paper 2023
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Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)
Isogeometric Analysis (IgA) can be seen as the natural extension of the Finite Element Method (FEM) to high-order B-spline basis functions. Combined with a time inte- gration scheme within the method of lines, IgA has become a viable alternative to FEM for time-dependent problems. However, as processors' clock speeds are no longer increasing but...
conference paper 2022
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Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)
The Material Point Method (MPM) has been applied successfully to problems in engineering which involve large deformations and history-dependent material behavior. However, the classical method suffers from some shortcomings which influence the quality of the numerical solution significantly. High-order B-spline basis functions solve the problem...
conference paper 2019
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Tielen, R.P.W.M. (author), Möller, M. (author), Vuik, Cornelis (author)
Introduced in [1], Isogeometric Analysis (IgA) has become widely accepted in academia and industry. However, solving the resulting linear systems remains a challenging task. For instance, the condition number of the Poisson operator scales quadratically with the mesh width h, but, in contrast to standard Finite Elements, exponentially with the...
conference paper 2018
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Wackers, J. (author), Koren, B. (author)
A surface capturing method is developed for steady water-air flow with gravity. Second-order accuracy is obtained with flux limiting and turbulence is modeled with Menter's model. The model is solved efficiently with a combination of multigrid and defect correction. Results for two test cases confirm the efficiency and accuracy of the method.
conference paper 2006
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Wackers, J. (author), Koren, B. (author)
A surface capturing method is developed for steady water-air flow with gravity. Second-order accuracy is obtained with flux limiting and turbulence is modeled with Menter's model. The model is solved efficiently with a combination of multigrid and defect correction. Results for two test cases confirm the efficiency and accuracy of the method.
conference paper 2006
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Scheichl, R. (author), Vainikko, E. (author)
We study two-level overlapping domain decomposition preconditioners with coarse spaces obtained by smoothed aggregation in iterative solvers for finite element discretisations of second-order elliptic problems. We are particularly interested in the situation where the diffusion coefficient (or the permeability) is highly variable throughout the...
conference paper 2006
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Anca, D. (author), Turek, S. (author), Wan, D. (author)
This paper discusses numerical simulation techniques using a moving mesh approach together with the multigrid fictitious boundary method (FBM) for liquid-solid flow configurations. The flow is computed by an ALE formulation with a multigrid finite element solver (FEATFLOW), and the solid particles are allowed to move freely through the...
conference paper 2006
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Darwish, M.S. (author), Saad, T. (author), Hamdan, Z. (author)
This paper deals with the implementation and performance analysis of a parallel Algebraic Multigrid Solver (pAMG) for a finite volume unstructured CFD code. The parallelization of the solver is based on the domain decomposition approach using the single program multiple data paradigm. The Message passing interface Library (MPI) is used for...
conference paper 2006
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Bin Zubair, H. (author), Oosterlee, C.W. (author)
This paper discusses multigrid for high dimensional partial differential equations (PDEs). We present partial grid-coarsening strategies for excellent multigrid convergence in the context of elliptic PDEs. We show that the multigrid convergence rate can satisfactorily be brought down with the grid strategies proposed herein, coupled with...
conference paper 2006
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Wan, J.W.L. (author)
In the paper, we present multigrid methods for solving scalar conservation laws and convection diffusion equations that frequently arise from fluid flow problems. For scalar conservation laws, we present monotonicity preserving and total variation diminishing multigrid methods. We generalize the upwind-biased residual restriction and...
conference paper 2006
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Gaspar, F.J. (author), Lisbona, F.J. (author), Oosterlee, C.W. (author)
In this work, we present a robust and efficient multigrid solver for a reformulated version of the system of poroelasticity equations. The reformulation enables us to treat the system in a decoupled fashion. It is sufficient to choose a highly efficient multigrid method for a scalar Poisson type equation for the overall solution of this...
conference paper 2006
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Beaudoin, A. (author), De Dreuzy, J.R. (author), Erhel, J. (author)
Subsurface hydraulic properties are mainly governed by the heterogeneity of the porous medium considered. Our work aims at characterizing the asymptotic dispersion coefficients for highly heterogeneous permeability fields triggered by advection and constant local dispersion-diffusion. We have developed a fully parallel software for simulating...
conference paper 2006
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Erlangga, Y.A. (author)
This paper discusses an iterative method for solving the Helmholtz equation with the perfectly matched layer (PML). The method consists of an outer and inner iteration process. The inner iteration is used to approximately solve a preconditioner, which in this case is based on a modified PML equation. The outer iteration is a Krylov subspace...
conference paper 2006
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De Borst, R. (author), Hulshoff, S.J. (author), Lenz, S. (author), Munts, E.A. (author), Van Brummelen, E.H. (author), Wall, W.A. (author)
The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have...
conference paper 2006
document
Bin Zubair, H. (author), Oosterlee, C.W. (author)
This paper discusses multigrid for high dimensional partial differential equations (PDEs). We present partial grid-coarsening strategies for excellent multigrid convergence in the context of elliptic PDEs. We show that the multigrid convergence rate can satisfactorily be brought down with the grid strategies proposed herein, coupled with...
conference paper 2006
document
Borzi, A. (author), Wogrin, M. (author)
Recent developments on multilevel schemes for open-loop optimal control problems with terminal observation governed by time-dependent reaction-diffusion systems are presented. The solution of optimality systems consisting of reaction-diffusion equations with opposite time orientation is discussed. Of particular importance in applications and for...
conference paper 2006
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Jönsthövel, T.B. (author), Oosterlee, C.W. (author), Mulder, W.A. (author)
We evaluated multigrid techniques for 3D diffusive electromagnetism. The Maxwell equations and Ohm's law were discretised on stretched grids, with stretching in all coordinate directions. We compared standard multigrid to alternative multigrid approaches with linewise smoothing and semi-coarsening, both as a stand-alone solver and as a...
conference paper 2006
document
Gaspar, F.J. (author), Lisbona, F.J. (author), Oosterlee, C.W. (author)
In this work, we present a robust and efficient multigrid solver for a reformulated version of the system of poroelasticity equations. The reformulation enables us to treat the system in a decoupled fashion. It is sufficient to choose a highly efficient multigrid method for a scalar Poisson type equation for the overall solution of this...
conference paper 2006
document
Hillewaert, K. (author), Remacle, J.F. (author), Cheveaugeon, N. (author), Bernard, P.E. (author), Geuzaine, P. (author)
A hybrid implicit and explicit p-Multigrid iteration strategy for the discretisation of the steady Euler equations with the discontinuous Galerkin finite element method is presented. The implicit strategy consists of an inexact damped Newton iteration, using an ILU(0)-preconditioned GMRES method for the solution of the linear system. Since the...
conference paper 2006
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