intermediate mass black hole and numerical relativity zhoujian cao institute of applied mathematics,...
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intermediate mass black hole and numerical relativity
Zhoujian Cao Institute of Applied Mathematics, AMSS 2013-7-1
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Category of Black Holes
• Super massive black hole:
M: 10^5—10^9 Msun
• Stellar massive black hole:
M: 1-10s Msun
• Intermediate massive black hole:
M: 10s—10^5 Msun (mainly in globular cluster)
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Category of Black Holes Binary
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ALIA
Xuefei Gong, et al, CQG 28, 094012 (2011)
1:1000
1:1
Advanced LIGO
Abadie, et al, PRD 85, 102004 (2012)
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Wave form template for GW detection
• PN templates: for early stage of inspiralling• EOBNR (effective one body model together
with numerical relativity): for full inspiral + merger + ring down stage; works well for mass ratio less than 1:8 and extreme mass ratio BBH
• But no reliable template for mass ratio 1:10 to 1:1000
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From a given separation of the two BHs, when mass ratio increases the number of orbit increases quickly. This requires that the numerical simulation with full GR increases much consequently. In contrast to 1:1, 1:100 needs 10 times more computation cost.
PN estimation
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Computational cost
1:1, 9 days 1:100, 20 days
LSSC cluster II, 128 CPUs, for last 2 orbits computational cost 1 to 20!!
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Challenge of large mass BBH to NR
• Compared to 1:1, the computational cost of 1:100 BBH increase roughly 200 times!!
• For typical simulation of 1:1 BBH, 14 days are needed. So by straight forward method to 1:100, roughly 1year is needed!!
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Possible ways out
• 1. Physical level: approximation method, such as self force frame work (but still first order yet), ……
• 2. Numerical Algorithm level: implicit scheme [R. Lau et al, PRD 84, 084023 (2011)], combine Cauchy evolution to null evolution, ……
• 3. Computer level: improve scalability to use more CPUs, use GPU, ……
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Possible ways out
• 1. Physical level: approximation method, such as self force frame work (but still first order yet), ……
• 2. Numerical Algorithm level: implicit scheme [R. Lau et al, PRD 84, 084023 (2011)], combine Cauchy evolution to null evolution, ……
• 3. Computer level: improve scalability to use more CPUs, use GPU, ……
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Mesh refinement scheme
F. Loeffler et al, CQG 29, 115001 (2012)
Level #2 Level #1
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Parallel mesh level algorithmCompared to traditional mesh refinement method, we can improve the scalability of the code and get 2x speed up
Cowork with Zhihui Du, S. Brandt and F. Loeffler, 2013
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GPU acceleration
For system biology, Yamazaki, Igarashi, Neural Networks, 2013
For GW data analysis, Zhihui Du, et al, CQG 29, 235018 (2012)
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Einstein solver with GPU
Cowork with Quan Yang, Zhihui Du, 2012
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Structure of AMSS-NCKU GPU code
Two groups MPI processes, one for cpu and one for gpu
MPI + OpenMP + CUDA
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Primary test of AMSS-NCKU GPU code
Titan: top 1 super computer around the world (now Tianhe 2)
1024x16 cores + 1024 GPUs
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Summary
• Challenge from GW detection:
AdvLIGO—1:150
ALIA ---1:1000
• Parallel mesh level calculation method—2x speed up
• GPU implementation to NR---have got roughly 5x speed up; 30x speed up? in progress