Full HTML for

Basic foilset Overview of BBH Simulations

Given by Scott Klasky at Physics Colloquium on Oct 29 1998. Foils prepared Jan 31 99
Outside Index Summary of Material

Physics Colloquium Oct 29 1998 based on Binary Black Hole (BBH) Computational Grand Challenge
1. Understand black holes & gravity waves
2. Learn the Einstein field equations
3. Convert eqns. To eqns. We evolve numerically
4. Model these equations on a computer
5. Modeling black holes
6. Understand the inner boundary
7. Understand the outer boundary
8. Putting it together
9. Model the elliptic pde's
10. Build computational infrastructure
To really model 2 black holes, we better understand the "real" problems!!

Table of Contents for full HTML of Overview of BBH Simulations

 Denote Foils where Image Critical
Denote Foils where HTML is sufficient
1 10 Easy? Steps to Model a Black Hole
2 The 10 Steps
3 Step 0: Motivation
4 0: Background: Binary Black Hole Grand Challenge
5 0:astrophysical Sources of Gravitational Waves
6 0:Gravitational Wave Detectors
7 1: What Are Black Holes?
8 1:Event Horizons
9 1:Apparent Horizons
10 2:Einstein Field Equations
11 3: 3+1 Decomposition of Spacetime
12 3: ADM 3+1 Form
13 3:ADM 3+1 form (cont.)
14 3:Casual differencing
15 3:Description of causal differencing
16 3:Description of CD (continued)
17 4: Computational Solutions
18 4:Computational Solutions
19 4:Computational Solutions (cont.)
20 4:Computational Solutions (cont.)
21 5: Modeling Black Holes
22 5:Modeling Black Holes
23 5: Modeling black holes (picture)
24 5: Modeling black holes (picture)
25 6: The Inner Boundary
26 6: The Inner Boundary (cont.)
27 6: The inner boundary+causal differencing
28 6: Inner boundary + causal differencing
29 6: The Inner Boundary
30 7:Outer Boundary
31 7:Blended Dirchlet Outer boundary
32 8: Putting it together
33 8:Non-Moving Black Holes (Centered)
34 8:Non-Moving Black Holes (Centered)
35 8:Non-Moving Black Holes (Centered)
36 8:Non-Moving Black Holes (Centered)
37 8:Boosted Black Holes
38 8:Boosted Black Holes
39 9:Elliptic Problems
40 10:Computational Infrastructure
41 10: DAGH
42 10: Visualization Software (Ki, Klasky)
43 10: SV2 System Architecture
44 Major Obstacles

Outside Index Summary of Material

HTML version of Basic Foils prepared Jan 31 99

Foil 1 10 Easy? Steps to Model a Black Hole

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Scott A. Klasky
NPAC (Syracuse University)
In collaboration with
Geoffrey Fox, Mijan Huq, Pablo Laguna, and Richard Matzner
And the binary black hole grand challenge alliance
Supported by NSF PHY 9318152 (ARPA supplemented), NSF PHY9310083 and Cray research
HTML version of Basic Foils prepared Jan 31 99

Foil 2 The 10 Steps

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
0. Motivate
1. Understand black holes & gravity waves
2. Learn the Einstein field equations
3. Convert eqns. To eqns. We evolve numerically
4. Model these equations on a computer
5. Modeling black holes
6. Understand the inner boundary
7. Understand the outer boundary
8. Putting it together
9. Model the elliptic pde's
10. Build computational infrastructure
To really model 2 black holes, we better understand the "real" problems!!
HTML version of Basic Foils prepared Jan 31 99

Foil 3 Step 0: Motivation

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Computational solution to the Einstein Field Equations for the purposes of modeling black hole spacetimes.
Binary Black Hole mergers provide strong detectable sources of gravitational radiation.
Accurate predictions of waveforms expected to enhance the detectability of gravity waves, build database of waveforms
Computational simulations of black hole mergers are important for accurate detection and characterization of GW.
Simulations of Binary Black Hole mergers will provide insights into strong field GR as well as provide a solution to the two-body problem of GR.
HTML version of Basic Foils prepared Jan 31 99

Foil 4 0: Background: Binary Black Hole Grand Challenge

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Alliance of 8 universities with the charter to predict gravitational radiation waveforms from binary black hole mergers.
Problem broken up into components.
Interior evolution (strong field region).
  • Development and construction of a Cauchy code .
  • Implementing black hole excision.
Outer boundary matching to characteristic exterior code.
  • Extracts waveforms.
  • Provides outer boundary conditions for Cauchy code.
HTML version of Basic Foils prepared Jan 31 99

Foil 5 0:astrophysical Sources of Gravitational Waves

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Coalescence of binary black holes .
  • Expected to be detected first. Detection will be enhanced by the presence of accurate predictions of waveforms to provide templates as well as a means of data analysis.
Coalescence of binary neutron stars.
Supernovae.
Other sources (stochastic background radiation).
HTML version of Basic Foils prepared Jan 31 99

Foil 6 0:Gravitational Wave Detectors

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Laser Interferometric Gravitational wave Observatory.
Ground-based detectors (GEO,VIRGO and one in Japan).
Space-based detectors (LISA and OMEGA).
Ability to detect astrophysical sources of gravitational radiation will bring about the possibility of gravitational wave astronomy.
HTML version of Basic Foils prepared Jan 31 99

Foil 7 1: What Are Black Holes?

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
A black hole is a region of spacetime from which it is not possible to communicate with "infinity".
Black holes are a possible endpoint of stellar evolution.
Black holes are predictions of Einstein's theory. They are vacuum solutions to the Einstein field equations.
Black holes contain curvature singularities contained within causal boundaries.
  • Cause computational problems in modeling them.
  • Can excise the interior of black holes to model them.
HTML version of Basic Foils prepared Jan 31 99

Foil 8 1:Event Horizons

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
The event horizon is the boundary in spacetime between those light rays that can escape to infinity and those that cannot.
  • Matter inside the event horizon is casually. disconnected from our universe and does not effect matter inside our universe.
  • A knowledge of the event horizon requires a knowledge of the entire spacetime.
  • To understand this we look at a model problem, the collapse of a star in spherical symmetry.
HTML version of Basic Foils prepared Jan 31 99

Foil 9 1:Apparent Horizons

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Apparent horizons are locatable with data at one instant of time. That is, they are local objects in contrast to event horizons which are global objects.
Apparent horizons provide an ideal surface for excision of the black hole singularity. Points inside the apparent horizon are causally disconnected from points exterior to it. Hence we use it to excise the curvature singularity within black holes.
The apparent horizon is defined by the solution of an elliptic equation.
HTML version of Basic Foils prepared Jan 31 99

Foil 10 2:Einstein Field Equations

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Relates the geometry of spacetime, as given by a spacetime metric, to mass-energy contained within it.
  • The gravitational field is the history of the geometry of a space-like hypersurface.
Matter/Energy curves spacetime and that in turn affects trajectories in it. For example:
  • Precession of Mercury's orbit.
  • Deflection of light around the Sun.
Black Holes are vacuum solutions (i.e.: Tmn= 0 )
  • Interaction of binary black holes occurs via their curvatures.
Gmn = kTmn
HTML version of Basic Foils prepared Jan 31 99

Foil 11 3: 3+1 Decomposition of Spacetime

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Pose the Einstein Field Equations as a Cauchy problem
  • Take the spacetime theory and manipulate the equations to equations which we can numerically model.
  • Slice spacetime into a series of "spacelike" slices in "time".
  • Four degrees of freedom in choosing "coordinate conditions"
HTML version of Basic Foils prepared Jan 31 99

Foil 12 3: ADM 3+1 Form

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
A relationship between the components of the metric of spacetime and those of the spatial 3-metric are defined.
We can look at the (ADM) form of the metric to see this:
ds2 = - a2dt2+gij(dxi+bidt)(dxj+b jdt),
where the functions a and bi are called the lapse and shift functions, and gij is the 3-metric
a determines the lapse in proper time, and bi describes the shift in the spatial coordinates, and ti are the tangents to a coordinate observer (moving through the spacetime moves timelike direction by a dt, and spacelike direction by b i).
HTML version of Basic Foils prepared Jan 31 99

Foil 13 3:ADM 3+1 form (cont.)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
The extrinsic curvature is a spacelike object which determines the contraction and shear of the normals to the hypersurface.
We can rewrite the ADM equations as:
  • ¶t gij = Lb gij - 2 a Kij
  • ¶t Kij = Lb Kij - Di Dj a + a(Rij + K Kij -2Kli Klj
  • where Lb Kij = bk ¶kKij + Kkj ¶i bk + Kik ¶jbk
Causal Differencing:
  • Before we describe causal differencing, a key ingredient for the evolution of black holes, we must state the desired properties of a black hole evolution scheme.
HTML version of Basic Foils prepared Jan 31 99

Foil 14 3:Casual differencing

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Evolve only the exterior of the hole, ignore interior.
  • No boundary condition should be imposed at the horizon.
Coordinates are well-behaved:
  • Coordinates do not fall into a stationary hole
  • Hole is allowed to move through the grid.
  • Requires large shift vector: difficult in computations.
Using CD, quantities are evolved along the center of the local light cone, then placed at their spatial locations.
Casual differencing allows for arbitrary choice of shift vector, makes the courant condition independent of the shift, naturally handles black hole excision, moving holes.
HTML version of Basic Foils prepared Jan 31 99

Foil 15 3:Description of causal differencing

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Canonical coordinate system denoted by (t,xi):Lt=¶/¶t
  • Spatial coordinates dragged along tm = anm + bm.
  • For quantities defined in (t,xi) basis, Lt = ¶ /¶t .
Introduce new coordinates :
  • Time coordinates coincide: .
  • Spatial coordinates dragged along normal vector norm nm
  • At the beginning of each step, t=t0, we set = xi.
HTML version of Basic Foils prepared Jan 31 99

Foil 16 3:Description of CD (continued)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Break up evolution into 2 smaller steps:
  • Evolve along normal vector norm anm, using coordinates.
    • (¶ /¶ t - Lb) T - ¶ / ¶ xi Si = R
    • rewrite as
    • components of spatial tensors are defined in xi basis, but evolved along paths of constant .
  • Interpolate to desired locations in canonical coordinate system.
HTML version of Basic Foils prepared Jan 31 99

Foil 17 4: Computational Solutions

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
We use 3D rectangular grids with Cartesian coordinates
Finite differencing to O(h2) in space
  • Utilize centered differencing to O(h2)
  • At the inner boundary use centered differencing where possible otherwise use one-sided differencing
HTML version of Basic Foils prepared Jan 31 99

Foil 18 4:Computational Solutions

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Use Iterative Crank-Nicholson time update scheme.
Code has provisions for both 2-level and 3-level time update schemes
Convergence tested with a variety of model spacetimes, (Linearized GW, black hole spacetimes, Cosmological spacetimes, etc) and found to be O(h2)
HTML version of Basic Foils prepared Jan 31 99

Foil 19 4:Computational Solutions (cont.)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
2 original versions of the code: FORTRAN 90 computational kernel with FORTRAN 90 and C++ DAGH (MPI based) front-ends (i.e.: serial and parallel versions).
  • DAGH (Distributed Adaptive Grid Hierarchy) will enable us to implement Parallel Adaptive Mesh Refinement
A new version of the code, AGAVE, is being developed which uses the Cactus (Postdam) front end, and provides linear speedup on Multiple processors.
HTML version of Basic Foils prepared Jan 31 99

Foil 20 4:Computational Solutions (cont.)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Storage requirements
  • Fundamental variables 16 times 2 (2-level) = 32.
  • Total ~130 3D Arrays or 2.2GB for a 129^3 grid.
  • Difficulties with "good" resolution.
  • Difficulties with placing boundaries .
  • AMR will help here.
Computationally expensive.
  • Current serial version takes days to run on a T90.
  • Eventual computation will be a ~teraflop calculation.
HTML version of Basic Foils prepared Jan 31 99

Foil 21 5: Modeling Black Holes

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Boundary conditions
  • Asymptotic flatness or that gij dij and Kij 0 at outer boundary. For model problem we use "Dirichlet conditions" or "blended boundary conditions" (later).
  • Inner boundary: excised interior of Apparent Horizon minus a number of buffer zones (will clarify). There is no boundary condition here; "Boundary without boundary conditions"
We believe that for 1 hole we understand how to model the inner boundary "Boosted 3-dimensional Black-Hole Evolutions with Singularity Excision", w/ G.B. Cook et al., Phys. Rev Lett, Vol 80, Number 12 (1998).
HTML version of Basic Foils prepared Jan 31 99

Foil 22 5:Modeling Black Holes

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Eventually outer boundary will be matched to an exterior evolution code that evolves the geometry along outgoing characteristics
  • Code will extract radiation waveforms
  • Evolve data out to "future null infinity"
  • Null code exists and can evolve black hole spacetimes "forever" or 60,000M. However stabily matching the two codes is a problem and once that is resolved we can utilize that module as an outer boundary condition on our Cauchy evolution.
HTML version of Basic Foils prepared Jan 31 99

Foil 23 5: Modeling black holes (picture)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Wave Extraction at infinity
Cauchy Code
Outer module
HTML version of Basic Foils prepared Jan 31 99

Foil 24 5: Modeling black holes (picture)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Dirchlet
blended
excised
HTML version of Basic Foils prepared Jan 31 99

Foil 25 6: The Inner Boundary

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Causal structure of Black holes such that no boundary conditions are required at and inside the apparent horizon of the black hole.
Require a good choice of "coordinates" in order to take advantage of this
The only problems that we have been able to do, have been "model problems" which give us coordinate conditions for static rotating, moving black holes (Choice corresponds to the Kerr-Schild spacetime metric or ingoing Eddington-Finkelstein coordinates for Schwarzschild black holes)
HTML version of Basic Foils prepared Jan 31 99

Foil 26 6: The Inner Boundary (cont.)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
The Schwarzschild (Ingoing Eddington-Finklestein) and Kerr spacetimes use the Kerr-Schild form of the metric:
  • The metric is form invariant under a boost.
  • The 3+1 decomposition are unique for boosted Schwarzschild or Kerr.
  • 3+1 decomposition gives us initial data (gij, Kij) and coordinate conditions (a,bi) which we can then use.
  • The analytical apparent horizon location is known everywhere.
HTML version of Basic Foils prepared Jan 31 99

Foil 27 6: The inner boundary+causal differencing

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
For a time-independent hole the algorithm is as follows:
  • Evolve data long normal using two-level scheme
  • Evolve values of uniform xi grid points along
  • Interpolate data from uniform points to uniform xi points .
  • For the innermost points we ignore them via extrapolation.
HTML version of Basic Foils prepared Jan 31 99

Foil 28 6: Inner boundary + causal differencing

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
The only difference for an advecting hole is that
  • Grid points on the leading edge of the hole are swallowed.
  • Grid points on the trailing edge emerge from the hole
For the emerging point, we can either extrapolate bi or extrapolate
HTML version of Basic Foils prepared Jan 31 99

Foil 29 6: The Inner Boundary

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Stability of the inner boundary: Sources of problems
  • Finite difference instabilities
  • Enforcing coordinate conditions so that coordinate pathologies do not develop.
Current research efforts are on interpolation techniques
  • Want O(h4) interpolations to get second order results.
    • Problem is getting symmetric stencils.
HTML version of Basic Foils prepared Jan 31 99

Foil 30 7:Outer Boundary

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
3 methods
  • 1. Blended Dirichlet outer boundary conditions.
    • Stable evolutions can be obtained!
    • Only works for limited cases with exact CC.
  • 2. Perturbative OB PRL 80 (1998) 1812-1815
    • Easier than CCM, since perturbative calculations are not expensive, and the matching is not complex.
    • Problems are that it needs to be far from the hole ~20M, and we need separate backgrounds from perturbations.
  • 3. Cauchy-characteristic matching (PRL 80 (1998) 3915-3918)
    • Works well for simple test cases.
HTML version of Basic Foils prepared Jan 31 99

Foil 31 7:Blended Dirchlet Outer boundary

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Evolves "forever" with the following model problem
Schwarzschild (Ingoing Eddington-Finkelstein) and Kerr spacetimes used.
Inner boundary differencing done to O(h2) with the truncation error matched to centered differencing operators.
Excised 2-sphere of radius r0=2M-ph(h=grid spacing, p=number of buffer zones).
Blended shell of inner and outer radii, R0 and R1,
  • r> R1 Dirichlet values
  • R0<r<R1 Blending
  • R<= R0 Cauchy
HTML version of Basic Foils prepared Jan 31 99

Foil 32 8: Putting it together

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Broke down the problem into a series of experiments
  • Placing a different number of buffer zones in AH.
  • Evolve moving black holes
  • Using outer boundary conditions improve evolutions.
Longest running 3D evolution of static black hole.
Cauchy evolution of a propagating hole
  • Black hole excision is indeed practical and feasible in a situation where the excised regions propagate through the computational domain
  • Issue is now with maintaining coordinate conditions and less with finite difference stability at the inner boundary
HTML version of Basic Foils prepared Jan 31 99

Foil 33 8:Non-Moving Black Holes (Centered)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Place the black hole in a computational grid of 49x49x49 points.
Excise the singularity with a buffer region of p points inside the apparent horizon (r=2M). Dirichlet outer boundary conditions.
ph
2M
8M
HTML version of Basic Foils prepared Jan 31 99

Foil 34 8:Non-Moving Black Holes (Centered)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Found a dependency on number of buffer zones utilized
  • p=1 tmax~ 20M
  • p=5 tmax~95M
  • p=9 tmax~82M
Find that the problem seems to be with coordinate conditions. Ripple from outer boundary travels inwards, excites the inner boundary. Repeated instances lead to coordinate drifting and an eventual coordinate pathology
HTML version of Basic Foils prepared Jan 31 99

Foil 35 8:Non-Moving Black Holes (Centered)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Introduced a "blending" region shown (exaggerated) by the shaded shell above
Linearly interpolated between computed and exact solution
HTML version of Basic Foils prepared Jan 31 99

Foil 36 8:Non-Moving Black Holes (Centered)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Found that by "smoothing" out the outer boundary that we were able to prolong and in some cases apparently lead to stable evolutions.
Find that the "proper" imposition of coordinate effects may be required. Our exact specification seems to be leading to coordinate drifting and hence our inner boundary instability.
One set of runs where results converge to a static solution (taken to be stable. Changes go down towards roundoff).
Longest prior evolutions due to Daues(~140M).
Problems occur when the outer boundary is at a large M.
HTML version of Basic Foils prepared Jan 31 99

Foil 37 8:Boosted Black Holes

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Grid size: 33x33x65 (h=1/4).
Boost in z-direction with a velocity of 0.1c .
Dirichlet Outer Boundaries as a function of time.
Lapse and shift (coordinate conditions) determined from exact expressions imposed as a function of time
Utilized 5 buffer regions inside of apparent horizon to place the the inner boundary
Dirichlet outer boundary conditions.
HTML version of Basic Foils prepared Jan 31 99

Foil 38 8:Boosted Black Holes

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Found that we can "move" a black hole (an excised region) for 3 black hole radii.
Importance here is that we can correctly propagate the black hole such that points that were previously excised are causally updated.
Data show that trailing end of black hole is smoothly update.
Problems however, with coordinate conditions.
Phys.Rev.Lett. 80 (1998) 2512-2516
Picture1, Picture 2
Movie 1, Movie 2
HTML version of Basic Foils prepared Jan 31 99

Foil 39 9:Elliptic Problems

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Simple Examples used Ingoing Eddington Finkelstein Coords.
Previously, for 2 black holes, we tried to use Isotropic Schwarzschild).
If we want to use "EF-like" coordinates, then we need new prescription to solve equations.
Hamiltonian.
Momentum.
Maximal Slicing
Min. Distortion
Boundary Conditions!!!! (Elliptics Need a boundary Eqn)
HTML version of Basic Foils prepared Jan 31 99

Foil 40 10:Computational Infrastructure

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Requirements:
  • 2 Black Holes, orbiting each other at first, and then coalescing.
  • Require the outer boundary of the cauchy code to be at least 8M away from the inner boundary.
  • Require the inner boundaries have sufficient resolution.
Need: A parallel code which uses Adaptive Mesh Refinement.
  • At the time of the onset of the BBH grand challenge there was no infrastructure to help us.
  • Browne, Parashar developed DAGH (Distributed Adaptive Grid Hierarchies).
HTML version of Basic Foils prepared Jan 31 99

Foil 41 10: DAGH

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Distributed dynamic data-structures for Parallel Hierarchical AMR
  • Transparent access to scalable distributed dynamic Arrays/Grids/Grid-Hierarchies
  • Multigrid/Line-Multigrid support within AMR
  • Shadow grid hierarchy for on-the-fly error estimation
  • Automatic dynamic partitioning and Load distribution
  • Locality, Scalablility, Portability, Performance
High-Level Programming Abstractions for AMR
  • Application Objects => Abstract Data Types
  • Coarse-grained data parallelism
  • Fortran compliant data storage
  • Intuitive, Easy-to-use, Performance
Checkpoint/Restart Support
HTML version of Basic Foils prepared Jan 31 99

Foil 42 10: Visualization Software (Ki, Klasky)

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
SV2: The next generation of Scivis.
Requirements
  • Support for animation of finite difference solutions for time-evolving systems.
  • X,Y plots, Contour Plots, Isosurfaces, Ray-tracing
  • PORTABILITY!!!!
  • COLABORATION!
  • User Definable Filters
  • Interactive visualization.
  • Presentation Quality output.
  • Reusability of current visualization routines.
  • Picture1, Picture 2
HTML version of Basic Foils prepared Jan 31 99

Foil 43 10: SV2 System Architecture

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Simulation
SV2 Server
Ray Tracing
Isosurfaces
Simple
User Definable
Filters
Scivis
Client
VRML Client
HTML version of Basic Foils prepared Jan 31 99

Foil 44 Major Obstacles

From Overview of BBH Simulations Physics Colloquium -- Oct 29 1998. *
Full HTML Index
Gauge Conditions (Coordinate Conditions).
  • Examples of Gauge Conditions
    • Maximal slicing
    • Minimal Distortion Shift
  • These equations are elliptic! (boundary conditions)
We want to construct the Lapse and shift that:
  • Minimize grid stretching; Help causal differencing
  • Not too expensive to compute
  • adapt to outer boundary
  • Questions: Hyperbolic Formalisms, other ADM formalisms, GAUGE conditions!!!!!!!!!
Blending energy from normal deflection
© Northeast Parallel Architectures Center, Syracuse University, npac@npac.syr.edu

If you have any comments about this server, send e-mail to webmaster@npac.syr.edu.

Page produced by wwwfoil on Sun Jan 31 1999