4,117 research outputs found
Achieving Extreme Resolution in Numerical Cosmology Using Adaptive Mesh Refinement: Resolving Primordial Star Formation
As an entry for the 2001 Gordon Bell Award in the "special" category, we
describe our 3-d, hybrid, adaptive mesh refinement (AMR) code, Enzo, designed
for high-resolution, multiphysics, cosmological structure formation
simulations. Our parallel implementation places no limit on the depth or
complexity of the adaptive grid hierarchy, allowing us to achieve unprecedented
spatial and temporal dynamic range. We report on a simulation of primordial
star formation which develops over 8000 subgrids at 34 levels of refinement to
achieve a local refinement of a factor of 10^12 in space and time. This allows
us to resolve the properties of the first stars which form in the universe
assuming standard physics and a standard cosmological model. Achieving extreme
resolution requires the use of 128-bit extended precision arithmetic (EPA) to
accurately specify the subgrid positions. We describe our EPA AMR
implementation on the IBM SP2 Blue Horizon system at the San Diego
Supercomputer Center.Comment: 23 pages, 5 figures. Peer reviewed technical paper accepted to the
proceedings of Supercomputing 2001. This entry was a Gordon Bell Prize
finalist. For more information visit http://www.TomAbel.com/GB
A Continuous Mesh Model for Discontinuous Petrov-Galerkin Finite Element Schemes with Optimal Test Functions
We present an anisotropic mesh adaptation strategy using a continuous
mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with
optimal test functions, extending our previous work on adaptation. The
proposed strategy utilizes the inbuilt residual-based error estimator of the
DPG discretization to compute both the polynomial distribution and the
anisotropy of the mesh elements. In order to predict the optimal order of
approximation, we solve local problems on element patches, thus making these
computations highly parallelizable. The continuous mesh model is formulated
either with respect to the error in the solution, measured in a suitable norm,
or with respect to certain admissible target functionals. We demonstrate the
performance of the proposed strategy using several numerical examples on
triangular grids.
Keywords: Discontinuous Petrov-Galerkin, Continuous mesh models,
adaptations, Anisotrop
Parallel software tool for decomposing and meshing of 3d structures
An algorithm for automatic parallel generation of three-dimensional unstructured computational meshes based on geometrical domain decomposition is proposed in this paper. Software package build upon proposed algorithm is described. Several practical examples of mesh generation on multiprocessor computational systems are given. It is shown that developed parallel algorithm enables us to reduce mesh generation time significantly (dozens of times). Moreover, it easily produces meshes with number of elements of order 5 · 107, construction of those on a single CPU is problematic. Questions of time consumption, efficiency of computations and quality of generated meshes are also considered
Simulation of two- and three-dimensional viscoplastic flows using adaptive mesh refinement
This paper presents a finite element solver for the simulation of steady non-Newtonian flow problems, using a regularized Bingham model, with adaptive mesh refinement capabilities.
The solver is based on a stabilized formulation derived from the variational multiscale framework. This choice allows the introduction of an a posteriori error indicator based on the small scale part of the solution, which is used to drive a mesh refinement procedure based on element subdivision.
This approach applied to the solution of a series of benchmark examples, which allow us to validate the formulation and assess its capabilities to model 2D and 3D non-Newtonian flows.Postprint (author's final draft
The DPG-star method
This article introduces the DPG-star (from now on, denoted DPG) finite
element method. It is a method that is in some sense dual to the discontinuous
Petrov-Galerkin (DPG) method. The DPG methodology can be viewed as a means to
solve an overdetermined discretization of a boundary value problem. In the same
vein, the DPG methodology is a means to solve an underdetermined
discretization. These two viewpoints are developed by embedding the same
operator equation into two different saddle-point problems. The analyses of the
two problems have many common elements. Comparison to other methods in the
literature round out the newly garnered perspective. Notably, DPG and DPG
methods can be seen as generalizations of and
least-squares methods, respectively. A priori error analysis and a posteriori
error control for the DPG method are considered in detail. Reports of
several numerical experiments are provided which demonstrate the essential
features of the new method. A notable difference between the results from the
DPG and DPG analyses is that the convergence rates of the former are
limited by the regularity of an extraneous Lagrange multiplier variable
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