Optimal deflation in the linear solver for lattice QCD

Optimal deflation in the linear solver for lattice QCD

Project reference: 1504

The student(s) will work in the Lattice QCD group of Prof. C. Alexandrou at CaSToRC in Cyprus.The task of the student will be to optimize deflation in the open source twisted mass code tmLQCD (https://github.com/etmc/tmLQCD) for the Blue Gene architecture.The student will write an interface so the eigenvectors produced using the tmLQCD code are written and reused for further computation. The student will investigate ways to optimise reading and writing (I/O) time, e.g. using compression or reduced precision.

The physics goals of the project is to allow the study of hadron structure using twisted mass fermions with improved statistics at the physical point. The student will be involved in the study of the lower lying spectrum of the Dirac operator within the twisted mass fermion formulation of lattice QCD when a clover term is present. Projecting the low-lying space can lead to a speedup of the Conjugate Gradient (CG) method used to compute the inverse of the Dirac matrix, which is a sparse matrix of billion by billion dimensions for typical lattice QCD computations.

For further details on tmLQCD, please refer to the paper “tmLQCD: a program suite to simulate Wilson Twisted mass Lattice QCD” (http://arxiv.org/abs/0905.3331) and the following presentation (http://www.cyi.ac.cy/cscTalks/111Urbach.pdf).


CaSToRC (Deflated LQCD solver)


Project mentor: Giannis Koutsou and Constantia Alexandrou


Site Co-ordinator: Constantia Alexandrou


Learning Outcomes

Knowledge of methods for linear solvers and implementation on state-of-the art supercomputers. Introduction to advanced numerical methods and theoretical approaches used in Particle and Nuclear Physics. The student will also learn advanced programming with regards to Parallel I/O.


Student Prerequisites (compulsory)

Undergraduate degree in Physics with grade above average and good programming experience.


Student Prerequisites (desirable)

Knowledge of Theoretical High Energy Physics; Experience with parallel programming.


Training Materials
Lattice Gauge Theories-Introduction, Heinz J Rothe, World Scientific



  • Week 1: Introduction to the tmLQCD code (theory behind the code, compile and run test cases)
  • Week 2-3: Fine tuning of ARPACK compile parameters and interfacing to tmLQCD
  • Week: 4-6: Development of I/O code to package eigenvalues and eigenvectors computed by ARPACK for efficient reading and writing to disk. Different compression methods will be investigated such as even/odd partitioning.
  • Week 7: Documentation of code and submission to main Git branch.
  • Week 8: Final report including benchmarking results.


Final Product Description

Improved code. May lead to a publication in a high impact Physics journal.


Adapting the Project – Increasing the Difficulty

In typical calculations the eigenvectors and eigenvalues for both signs (+/-) of the bare quark mass parameter are required. If time permits, the student will investigate ways of computing the spectrum for both signs simultaneously.


Adapting the Project – Decreasing the Difficulty

The team has experts who can help the student(s) at all stages of the work.Should any difficulties arise, we will restrict the investigation in compression algorithms to a minimal set.



Access to JUQUEEN will be provided



Computation-based Science and Technology Research Center, The Cyprus Institute

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