Multi-block/multi-core SSOR preconditioner for the QCD quark solver for K computer

Understand

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.