Modified block BiCGSTAB for lattice QCD

Nakamura, Y.; Ishikawa, Ken-ichi; Kuramashi, Y.; Sakurai, Tetsuya; Tadano, Hiroshi

doi:10.1016/j.cpc.2011.08.010

Cited by 16 publications

(16 citation statements)

References 15 publications

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“…Besides that, in this experiment, the speedup factor is usually 30% higher than the MV ratio, which is robust to the optical property. This extra efficiency can be explained by the better memory cache usage of matrix-matrix multiplication in block BiCGStab as compared to multiple matrix-vector multiplications for multiple sources in sequential BiCGStab [44]. We can observe that the CPU time of the block BiCGStab is less dependent on optical property because it treats multiple right hand sides simultaneously and therefore the solution search through extended Krylov subspace rather than the matrix nature by optical properties is a dominant factor affecting the overall CPU time, whereas the sequential solver deals with multiple right-hand sides individually and thus the individual CPU time that highly depends on the optical properties determines the total CPU time.…”

Section: Numerical Resultsmentioning

confidence: 99%

Fast linear solver for radiative transport equation with multiple right hand sides in diffuse optical tomography

Jia

Kim

Hielscher

2015

Journal of Quantitative Spectroscopy and Radiative Transfer

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It is well known that radiative transfer equation (RTE) provides more accurate tomographic results than its diffusion approximation (DA). However, RTE-based tomographic reconstruction codes have limited applicability in practice due to their high computational cost. In this article, we propose a new efficient method for solving the RTE forward problem with multiple light sources in an all-at-once manner instead of solving it for each source separately. To this end, we introduce here a novel linear solver called block biconjugate gradient stabilized method (block BiCGStab) that makes full use of the shared information between different right hand sides to accelerate solution convergence. Two parallelized block BiCGStab methods are proposed for additional acceleration under limited threads situation. We evaluate the performance of this algorithm with numerical simulation studies involving the Delta-Eddington approximation to the scattering phase function. The results show that the single threading block RTE solver proposed here reduces computation time by a factor of 1.5~3 as compared to the traditional sequential solution method and the parallel block solver by a factor of 1.5 as compared to the traditional parallel sequential method. This block linear solver is, moreover, independent of discretization schemes and preconditioners used; thus further acceleration and higher accuracy can be expected when combined with other existing discretization schemes or preconditioners.

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Section: Numerical Resultsmentioning

confidence: 99%

Fast linear solver for radiative transport equation with multiple right hand sides in diffuse optical tomography

Jia

Kim

Hielscher

2015

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…Block solvers have been shown to provide large speedups in two recent lattice QCD studies of inverting the Dirac operator with multiple right hand side (RHS) vectors [21,25]. There are two sources of this speed-up: one is that as the number of RHS vectors (n pf in our case) is increased the number of iterations required for the solver to converge decreases, the other is that applying the Dirac operator to a block of vectors is significantly faster, since the cost of loading the gauge links is amortised over the many RHS vectors, and these data are contiguous allowing better use of the CPU cache.…”

Section: B Block Solversmentioning

confidence: 99%

“…Recently there has been renewed interest [19][20][21][22][23][24][25] in the use of block Krylov solvers [26], which invert the same matrix on multiple vectors simultaneously, and thanks to the enlarged Krylov basis from which solutions are constructed, can converge with significantly fewer iterations than are required to solve each vector separately.…”

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confidence: 99%

Rational hybrid Monte Carlo with block solvers and multiple pseudofermions

Forcrand

Keegan

2018

Phys. Rev. E

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The dominant cost of most lattice QCD simulations is the inversion of the Dirac operator required to calculate the force term in the RHMC update. One way to improve this situation is to use multiple pseudofermions, which reduces the size and variance of this force and hence allows a larger integration step size to be used. This means fewer force term calculations are required, but at the cost of having to invert the Dirac operator for each pseudofermion field. This bottleneck can be addressed: recently there has been renewed interest in the use of block Krylov solvers, which can solve multiple right hand side vectors with significantly fewer iterations than are required if each vector is solved using a separate Krylov solver. We combine these two ideas, achieving a significant speed-up of RHMC lattice QCD simulations.

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“…(2.2). The inversion algorithm for Dirac matrices is the block solver of [22] which accelerates by a factor of 3 ∼ 4 compared with non-block solvers.…”

Section: Methods For 1+1+1 Flavor Qcd+qed Simulation At the Physical Pmentioning

confidence: 99%