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Multi-block/multi-core SSOR preconditioner for the QCD quark solver for K computer
High Energy Physics - Lattice · Submitted 28 Oct 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We observe an ideal weak-scaling performance from 16 nodes to 4096 nodes.
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The abstract, sentence by sentence
We study the algorithmic optimization and performance tuning of the Lattice QCD clover-fermion solver for the K computer. We implement the L\"uscher's SAP preconditioner with sub-blocking in which the lattice block in a node is further divided to several sub-blocks to extract enough parallelism for the 8-core CPU SPARC64$^{\mathrm{TM}}$ VIIIfx of the K computer. To achieve a better convergence property we use the symmetric successive over-relaxation (SSOR) iteration with {\it locally-lexicographical} ordering for the sub-blocks in obtaining the block inverse. The SAP preconditioner is included in the single precision BiCGStab solver of the nested BiCGStab solver. The single precision part of the computational kernel are solely written with the SIMD oriented intrinsics to achieve the best performance of the \SPARC on the K computer. We benchmark the single precision BiCGStab solver on the three lattice sizes: $12^3\times 24$, $24^3\times 48$ and $48^3\times 96$, with fixing the local lattice size in a node at $6^3\times 12$. We observe an ideal weak-scaling performance from 16 nodes to 4096 nodes. The performance of a computational kernel exceeds 50% efficiency, and the single precision BiCGstab has $\sim26% susutained efficiency.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the algorithmic optimization and performance tuning of the Lattice QCD clover-fermion solver for the K computer. | contribution 0.96 | 0.89 | 0.05 | asserted 0.76 |
| s1 | We implement the L\"uscher's SAP preconditioner with sub-blocking in which the lattice block in a node is further divided to several sub-blocks to extract enough parallelism for the 8-core CPU SPARC64$^{\mathrm{TM}}$ VIIIfx of the K computer. | method 0.90 | 0.94 | 0.04 | asserted 1.00 |
| s2 | To achieve a better convergence property we use the symmetric successive over-relaxation (SSOR) iteration with {\it locally-lexicographical} ordering for the sub-blocks in obtaining the block inverse. | method 0.98 | 0.88 | 0.05 | asserted 0.97 |
| s3 | The SAP preconditioner is included in the single precision BiCGStab solver of the nested BiCGStab solver. | method 0.99 | 0.75 | 0.04 | asserted 1.00 |
| s4 | The single precision part of the computational kernel are solely written with the SIMD oriented intrinsics to achieve the best performance of the \SPARC on the K computer. | method 0.99 | 0.89 | 0.04 | asserted 1.00 |
| s5 | We benchmark the single precision BiCGStab solver on the three lattice sizes: $12^3\times 24$, $24^3\times 48$ and $48^3\times 96$, with fixing the local lattice size in a node at $6^3\times 12$. | method 0.98 | 0.96 | 0.04 | asserted 0.94 |
| s6 | We observe an ideal weak-scaling performance from 16 nodes to 4096 nodes. | result 1.00 | 0.96 | 0.31 | asserted 1.00 |
| s7 | The performance of a computational kernel exceeds 50% efficiency, and the single precision BiCGstab has $\sim26% susutained efficiency. | result 1.00 | 0.94 | 0.39 | asserted 1.00 |
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Original abstract
We study the algorithmic optimization and performance tuning of the Lattice QCD clover-fermion solver for the K computer. We implement the L\"uscher's SAP preconditioner with sub-blocking in which the lattice block in a node is further divided to several sub-blocks to extract enough parallelism for the 8-core CPU SPARC64$^{\mathrm{TM}}$ VIIIfx of the K computer. To achieve a better convergence property we use the symmetric successive over-relaxation (SSOR) iteration with {\it locally-lexicographical} ordering for the sub-blocks in obtaining the block inverse. The SAP preconditioner is included in the single precision BiCGStab solver of the nested BiCGStab solver. The single precision part of the computational kernel are solely written with the SIMD oriented intrinsics to achieve the best performance of the \SPARC on the K computer. We benchmark the single precision BiCGStab solver on the three lattice sizes: $12^3\times 24$, $24^3\times 48$ and $48^3\times 96$, with fixing the local lattice size in a node at $6^3\times 12$. We observe an ideal weak-scaling performance from 16 nodes to 4096 nodes. The performance of a computational kernel exceeds 50% efficiency, and the single precision BiCGstab has $\sim26% susutained efficiency.
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References
How the literature uses it
13 arXiv papers cite this in 13 sentences
Papers citing it · 3 sentences without a confident label
Uses its method or tool 10 papers
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The measurements of NBS correlators are performed at the unitary point, where the block solver [ref] is used for the quark propagator and unified contraction algorithm [ref] is used for the contraction.
Baryon interactions from lattice QCD with physical masses -- Overview and $S = 0, -4$ sectors -- · Lattice QCD setup · 1.00
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The measurements of NBS correlators are performed at the unitary point, where the block solver [ref] is used for the quark propagator and unified contraction algorithm [ref] is used for the contraction.
Baryon interactions from lattice QCD with physical quark masses -- Nuclear forces and $\Xi\Xi$ forces -- · Lattice QCD setup · 1.00
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Combined with the efficient solver for quark propagators [ref] , the performance efficiency for the total measurement computations achieves $∼$ 17% on 2048 nodes ($×$ 8 cores/node) of K computer, corresponding to $∼$ 45 TFlops sustained.
Towards Lattice QCD Baryon Forces at the Physical Point: First Results · Lattice QCD setup · 0.94
What it cites · 5 sentences without a confident label
Uses the method or tool of 2 papers
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To extract 8 core parallelism for the K computer, we further divide the block into 16 sub-blocks via the locally-lexicographical ordering (ll-ordering) described in [ref] .
A Preconditioner for Improved Fermion Actions · Performance tuning for the K computer · 0.90
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We focus on the solver algorithm preconditioned by the domain-decomposed Schwartz alternating procedure (SAP) with mixed precision [ref] .
Schwarz-preconditioned HMC algorithm for two-flavour lattice QCD · Lattice QCD on the K computer · 0.94
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