33 research outputs found
A new dissipation term for finite-difference simulations in Relativity
We present a new numerical dissipation algorithm, which can be efficiently
used in combination with centered finite-difference methods. We start from a
formulation of centered finite-volume methods for Numerical Relativity, in
which third-order space accuracy can be obtained by employing just
piecewise-linear reconstruction. We obtain a simplified version of the
algorithm, which can be viewed as a centered finite-difference method plus some
'adaptive dissipation'. The performance of this algorithm is confirmed by
numerical results obtained from 3D black hole simulations.Comment: Talk presented at the Spanish Relativity Meeting (Tenerife 2007
Constraint-preserving boundary conditions in the 3+1 first-order approach
A set of energy-momentum constraint-preserving boundary conditions is
proposed for the first-order Z4 case. The stability of a simple numerical
implementation is tested in the linear regime (robust stability test), both
with the standard corner and vertex treatment and with a modified
finite-differences stencil for boundary points which avoids corners and
vertices even in cartesian-like grids. Moreover, the proposed boundary
conditions are tested in a strong field scenario, the Gowdy waves metric,
showing the expected rate of convergence. The accumulated amount of
energy-momentum constraint violations is similar or even smaller than the one
generated by either periodic or reflection conditions, which are exact in the
Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly
given, which extends the parametric domain of symmetric hyperbolicity for the
Z4 formalism. The application of these results to first-order BSSN-like
formalisms is also considered.Comment: Revised version, with conclusive numerical evidence. 23 pages, 12
figure
Gowdy waves as a test-bed for constraint-preserving boundary conditions
Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a
test-bed for constraint-preserving boundary conditions in the non-linear
regime. As an illustration, energy-constraint preservation is separately tested
in the Z4 framework. Both algebraic conditions, derived from energy estimates,
and derivative conditions, deduced from the constraint-propagation system, are
considered. The numerical errors at the boundary are of the same order than
those at the interior points.Comment: 5 pages, 1 figure. Contribution to the Spanish Relativity Meeting
200
Linear high-resolution schemes for hyperbolic conservation laws: TVB numerical evidence
The Osher-Chakrabarthy family of linear flux-modification schemes is
considered. Improved lower bounds on the compression factors are provided,
which suggest the viability of using the unlimited version. The LLF flux
formula is combined with these schemes in order to obtain efficient
finite-difference algorithms. The resulting schemes are applied to a battery of
numerical tests, going from advection and Burgers equations to Euler and MHD
equations, including the double Mach reflection and the Orszag-Tang 2D vortex
problem. Total-variation-bounded behavior is evident in all cases, even with
time-independent upper bounds. The proposed schemes, however, do not deal
properly with compound shocks, arising from non-convex fluxes, as shown by
Buckley-Leverett test simulations.Comment: Revised version, including new tests to appear in Journal of
Computational Physic
A distributed multiscale computation of a tightly coupled model using the Multiscale Modeling Language
AbstractNature is observed at all scales; with multiscale modeling, scientists bring together several scales for a holistic analysis of a phenomenon. The models on these different scales may require significant but also heterogeneous computational resources, creating the need for distributed multiscale computing. A particularly demanding type of multiscale models, tightly coupled, brings with it a number of theoretical and practical issues. In this contribution, a tightly coupled model of in-stent restenosis is first theoretically examined for its multiscale merits using the Multiscale Modeling Language (MML); this is aided by a toolchain consisting of MAPPER Memory (MaMe), the Multiscale Application Designer (MAD), and Gridspace Experiment Workbench. It is implemented and executed with the general Multiscale Coupling Library and Environment (MUSCLE). Finally, it is scheduled amongst heterogeneous infrastructures using the QCG-Broker. This marks the first occasion that a tightly coupled application uses distributed multiscale computing in such a general way
Performance of distributed multiscale simulations
Multiscale simulations model phenomena across natural scales using monolithic or component-based code, running on local or distributed resources. In this work, we investigate the performance of distributed multiscale computing of component-based models, guided by six multiscale applications with different characteristics and from several disciplines. Three modes of distributed multiscale computing are identified: supplementing local dependencies with large-scale resources, load distribution over multiple resources, and load balancing of small- and large-scale resources. We find that the first mode has the apparent benefit of increasing simulation speed, and the second mode can increase simulation speed if local resources are limited. Depending on resource reservation and model coupling topology, the third mode may result in a reduction of resource consumption