Stretching the Limits of NR Bla Szilgyi, CalTech NRDA 2013 - - PowerPoint PPT Presentation

Stretching the Limits of NR

Béla Szilágyi, CalTech

NRDA 2013 September 18, 2013

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A new landscape in the “BBH business”

• After a long period of code development / optimization, the

SpEC/CCC code has gained significantly in its robustness and efficiency

–

Improved control of accuracy

–

Extended the region of parameter space where the code “just works” (spin ~ 0.95, q ~ 10 )

–

Evolution speed has gained significantly

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A new landscape in the “BBH business”

• After a long period of code development / optimization, the

SpEC/CCC code has gained significantly in its robustness and efficiency

–

Improved control of accuracy

–

Extended the region of parameter space where the code “just works” (spin ~ 0.95, q ~ 10 )

–

Evolution speed has gained significantly NRAR had a significant role in this – it forced us to pull our act

• together. We automated mergers, implemented AMR, etc.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A new landscape in the “BBH business”

• The long desired goal of “giving LIGO/VIRGO whatever

they could ever want for BBH” has come to within reach.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A new landscape in the “BBH business”

• The long desired goal of “giving LIGO/VIRGO whatever

they could ever want for BBH” has come to within reach.

• Plans are twofold:

1.

We want to produce a large number of “short” waveforms (<100 cycles)

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A new landscape in the “BBH business”

• The long desired goal of “giving LIGO/VIRGO whatever

they could ever want for BBH” has come to within reach.

• Plans are twofold:

1.

We want to produce a large number of “short” waveforms (<100 cycles)

1.

Will work on Reduced Order Modeling, to span out the 7d (8d?) space

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A new landscape in the “BBH business”

• The long desired goal of “giving LIGO/VIRGO whatever

they could ever want for BBH” has come to within reach.

• Plans are twofold:

1.

We want to produce a large number of “short” waveforms (<100 cycles)

1.

Will work on Reduced Order Modeling, to span out the 7d (8d?) space

2.

In principle any interpolation mechanism or search algorithm can specify its

• ptimized input points

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A new landscape in the “BBH business”

• The long desired goal of “giving LIGO/VIRGO whatever

they could ever want for BBH” has come to within reach.

• Plans are twofold:

1.

We want to produce a large number of “short” waveforms (<100 cycles)

1.

Will work on Reduced Order Modeling, to span out the 7d (8d?) space

2.

In principle any interpolation mechanism or search algorithm can specify its

• ptimized input points

This stage may require a few thousand well selected runs.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A new landscape in the “BBH business”

• The long desired goal of “giving LIGO/VIRGO whatever

they could ever want for BBH” has come to within reach.

• Plans are twofold:
• 1. Thousands of “short” waveforms
• 2. We plan to produce a selected set of “long” waveforms that reach

back into the valid PN region. The goal is to help EOB and/or

• ther semi-analytic models. We envision doing a few dozen of

these.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A new landscape in the “BBH business”

• The long desired goal of “giving LIGO/VIRGO whatever

they could ever want for BBH” has come to within reach.

• Plans are twofold:
• 1. Thousands of “short” waveforms
• 2. Dozens of “long” waveforms
• The various approaches would then be used to mutually

check one another.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A new landscape in the “BBH business”

• The long desired goal of “giving LIGO/VIRGO whatever

they could ever want for BBH” has come to within reach.

• Plans are twofold:
• 1. Thousands of “short” waveforms
• 2. Dozens of “long” waveforms
• The various approaches would then be used to mutually

check one another.

I’ll start with the “long” waveforms. I’ll talk about the “reduced basis” approach if time permits.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A 175 orbit, q=7 run

• Run pushed by Jonathan Blackman @ Caltech
• Low resolution just reached merger.

Need another few days for a full (low-res) waveform.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

A 175 orbit, q=7 run

• Run pushed by Jonathan Blackman @ Caltech
• Parameters:

–

Mass ratio 7, no spin

–

350+ GW cycles to merger

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Computational cost / efficiency

• 48 cores

–

A typical BBH run fits onto a laptop, scaling to a large number of cores is difficult Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Computational cost / efficiency

• 48 cores
• O(Tbytes) of disk

space

–

after post- processing this should decrease significantly Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Computational cost / efficiency

• 48 cores
• O(Tbytes) of disk

space On a new cluster, with the latest code, this could be O(2-4) faster.

Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Constraints

• Constraints drop

when AMR adds resolution.

• The spike is the

merger – the ringdown just started.

Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Orbital frequency

• Orbital frequency:

–

Initial: 6.792e-3

–

Merger: 2.44e-1 Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Orbital frequency

• Orbital frequency:

–

Initial: 6.792e-3

–

Merger: 2.44e-1

• The eccentricity is

0.00031, larger than usual.

Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Orbital frequency

• Orbital frequency:

–

Initial: 6.792e-3

–

Merger: 2.44e-1

• Convergence is

well preserved after >80 orbits.

Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Orbital phase

• The high

resolution phase error is < 0.1 radians at t = 67,000 M. (no alignment)

Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Apparent Horizon Separation

• Convergence and

eccentricity are both apparent.

Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Irreducible Mass

• AhA is doing well.
• The O(1e-5)

anomaly for AhB may be due to inaccurate AH finder settings.

–

If so, the overall run accuracy is not affected. Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Newtonian Center of Mass

• A long time-scale

drift is seen.

–

“short” runs could not have seen this

–

Waveforms will tell how much of this is gauge.

–

Could be an outer boundary effect

Colors: x, y, z

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Newtonian Center of Mass

• The oscillatory

behavior is largely related to the “Newtonian” definition

Colors: x, y, z

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Newtonian Center of Mass

• Junk Radiation

induced features seem to be well resolved

Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Newtonian Center of Mass

• Convergence is

well preserved for 80+ orbits

Colors: Lev0, Lev1, Lev2, Lev3

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Overlap with PN

Overlap T0 0.9986

• 60,000

0.9962

• 50,000

0.9888

• 40,000
• We calculated the PN overlap with

CCE waveforms, integrating up to some T0, measured back from merger.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Overlap with PN

Overlap T0 0.9986

• 60,000

0.9962

• 50,000

0.9888

• 40,000
• We calculated the PN overlap with

CCE waveforms, integrating up to some T0, measured back from merger.

• Eccentricity, drift must have had an effect

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Overlap with PN

Overlap T0 0.9986

• 60,000

0.9962

• 50,000

0.9888

• 40,000
• We calculated the PN overlap with

CCE waveforms, integrating up to some T0, measured back from merger.

• Overlap falls below 0.99 at T0 < - 40,000

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Summary of the long q=7 run

• This is a proof of principle.

We can now reach into PN land.

• These runs take months. We’ll
• nly do as many as helpful.
• Convergence is well preserved.
• We need to understand the

Newtonian COM drift.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Summary of the long q=7 run

• This is a proof of principle.

We can now reach into PN land.

• These runs take months. We’ll
• nly do as many as helpful.
• Convergence is well preserved.
• We need to understand the

Newtonian COM drift. The leading order SpEC issues no longer appear to be numerical.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

On the subject of “many short runs:”

This is work we’re pursuing@Caltech with

–

Jonathan Blackman

–

Chad Galley

–

Manuel Tiglio

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

On the subject of “many short runs:”

This is work we’re pursuing@Caltech with

–

Jonathan Blackman

–

Chad Galley

–

Manuel Tiglio

Technical details will be skipped. If in doubt, ask Scott Field.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Reduced Order Modeling in the BBH waveform space

• One main idea is to treat waveforms as vectors in

the “waveform space”

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Reduced Order Modeling in the BBH waveform space

• One main idea is to treat waveforms as vectors in

the “waveform space”

• Given enough different cows, you can express, to a

large accuracy, any new cow as a linear combination of the existing cows.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Reduced Order Modeling in the BBH waveform space

• One main idea is to treat waveforms as vectors in

the “waveform space”

• Given enough different cows, you can express, to a

large accuracy, any new cow as a linear combination of the existing cows.

• Waveforms are no different.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Reduced Order Modeling in the BBH waveform space

• One main idea is to treat waveforms as vectors in

the “waveform space”

• Given enough different cows, you can express, to a

large accuracy, any new cow as a linear combination of the existing cows.

• Waveforms are no different.
• The technique is known to converge exponentially

for smooth data.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

Reduced Order Modeling in the BBH waveform space

Challenges:

• High dimensional space (7d or 8d with eccentricity.)
• Need a place where one can push hundreds of

runs at once.

–

One run @ four resolutions needs 200 cores

–

Typical run-length can be weeks (depends on q, spin)

–

Logistics of post processing, etc.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

The two-fold approach to the BBH problem

Assume that all technicalities get sorted.

• The plan is full coverage of the waveform space

using RB / short waveforms.

• We want to provide EOB / phenom / …. with all

they need to get it right (including long runs).

• Then we can cross check.

Béla Szilágyi, Caltech NRDA 2013 Stretching the Limits of NR

The two-fold approach to the BBH problem

Assume that all technicalities get sorted.

• The plan is full coverage of the waveform space

using RB / short waveforms.

• We want to provide EOB / phenom / …. with all

they need to get it right (including long runs).

• Then we can cross check.

QUESTIONS?