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Adaptive Mesh Refinement

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Steven L. Liebling – One of the best experts on this subject based on the ideXlab platform.

  • Adaptive Mesh Refinement and Relativistic MHD
    arXiv: General Relativity and Quantum Cosmology, 2008
    Co-Authors: David Neilsen, Eric W. Hirschmann, Matthew Anderson, Steven L. Liebling
    Abstract:

    We solve the general relativistic magnetohydrodynamics equations using distributed parallel Adaptive Mesh Refinement. We discuss strong scaling tests of the code, and present evolutions of Michel accretion and a TOV star.

  • Relativistic MHD with Adaptive Mesh Refinement
    Classical and Quantum Gravity, 2006
    Co-Authors: Matthew Anderson, Eric W. Hirschmann, Steven L. Liebling, David Neilsen
    Abstract:

    This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel Adaptive Mesh Refinement (AMR). The fluid equations are solved using a finite difference convex ENO method (CENO) in 3 + 1 dimensions, and the AMR is Berger–Oliger. Hyperbolic divergence cleaning is used to control the ∇ ⋅ B = 0 constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.

  • The nonlinear sigma model with distributed Adaptive Mesh Refinement
    Classical and Quantum Gravity, 2004
    Co-Authors: Steven L. Liebling
    Abstract:

    An Adaptive Mesh Refinement scheme is implemented in a distributed environment using message passing interface to find solutions to the nonlinear sigma model. In a previous work, I studied the behaviour similar to black hole critical phenomena at the threshold for singularity formation in this flat-space model. The present study is a follow-up describing extensions to distribute the grid hierarchy and presenting tests showing the correctness of the model.

David Neilsen – One of the best experts on this subject based on the ideXlab platform.

  • Adaptive Mesh Refinement and Relativistic MHD
    arXiv: General Relativity and Quantum Cosmology, 2008
    Co-Authors: David Neilsen, Eric W. Hirschmann, Matthew Anderson, Steven L. Liebling
    Abstract:

    We solve the general relativistic magnetohydrodynamics equations using distributed parallel Adaptive Mesh Refinement. We discuss strong scaling tests of the code, and present evolutions of Michel accretion and a TOV star.

  • Relativistic MHD with Adaptive Mesh Refinement
    Classical and Quantum Gravity, 2006
    Co-Authors: Matthew Anderson, Eric W. Hirschmann, Steven L. Liebling, David Neilsen
    Abstract:

    This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel Adaptive Mesh Refinement (AMR). The fluid equations are solved using a finite difference convex ENO method (CENO) in 3 + 1 dimensions, and the AMR is Berger–Oliger. Hyperbolic divergence cleaning is used to control the ∇ ⋅ B = 0 constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.

Luca Antiga – One of the best experts on this subject based on the ideXlab platform.

  • An Adaptive Mesh Refinement solver for large‐scale simulation of biological flows
    International Journal for Numerical Methods in Biomedical Engineering, 2010
    Co-Authors: Lorenzo Alessio Botti, Marina Piccinelli, Bogdan Ene-iordache, Andrea Remuzzi, Luca Antiga
    Abstract:

    The observation that hemodynamic forces play an important role in the pathophysiology of the cardiovascular system has led to the need for characterizing in vivo hemodynamics on a patient-specific basis. However, the introduction of computational hemodynamics in clinical research contexts is bound to the availability of integrated workflows for analyses on large populations. Since such workflows must rely on automated geometry-driven Mesh generation methods, the availability of robust solvers featuring Adaptive Mesh Refinement strategies is essential to ensure that the approach can be adopted on a large scale. In this paper, we present an open-source solver for the incompressible Navier–Stokes equations based on the libMesh finite elements library, featuring Adaptive Mesh Refinement and parallelization. The solution scheme is a second-order velocity correction in rotational form. By presenting numerical tests on benchmark cases, we demonstrate that the coupling of this solution strategy with Adaptive Mesh Refinement leads to a solver with good accuracy characteristics despite the relative simplicity of the scheme adopted. The availability of this solver within the Vascular Modeling Toolkit project leads to a widely available, seamless pipeline from images to simulation ready to be applied in clinical research environments. Copyright © 2009 John Wiley & Sons, Ltd.

W Choptuikmatthew – One of the best experts on this subject based on the ideXlab platform.

  • Adaptive Mesh Refinement for coupled elliptic-hyperbolic systems
    Journal of Computational Physics, 2006
    Co-Authors: Pretoriusfrans, W Choptuikmatthew
    Abstract:

    We present a modification to the Berger and Oliger Adaptive Mesh Refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such …

Lisa L. Lowe – One of the best experts on this subject based on the ideXlab platform.

  • Multigrid elliptic equation solver with Adaptive Mesh Refinement
    Journal of Computational Physics, 2005
    Co-Authors: J. David Brown, Lisa L. Lowe
    Abstract:

    In this paper, we describe in detail the computational algorithm used by our parallel multigrid elliptic equation solver with Adaptive Mesh Refinement. Our code uses truncation error estimates to Adaptively refine the grid as part of the solution process. The presentation includes a discussion of the orders of accuracy that we use for prolongation and restriction operators to ensure second order accurate results and to minimize computational work. Code tests are presented that confirm the overall second order accuracy and demonstrate the savings in computational resources provided by Adaptive Mesh Refinement.