Fellow: ESR5 
Host institution: UCY 
Ph.D. enrolment: UCY and BUW 
Project Title: Scalable algorithms for solvers and noise reduction techniques for disconnected quark loops in lattice QCD 
Objectives: Two components contribute to the very high computational cost for the calculation of disconnect quark loops in lattice QCD: the numerical cost due to the repeated solves of illconditioned linear systems and the statistical cost, which requires many systems to be solved to keep the statistical error below the required threshold. The purpose of this project is to reduce this computational cost by providing an approximation to the operator, which can be inverted directly or very efficiently and at the same time reduce the statistical noise of the remaining part of the operator. We aim at having the contribution of this part to the inverse to be small, so that a relatively large statistical error contributes only little to the overall error, thereby reducing the work on the statistics part. Current approaches in this direction rely on the explicit deflation of small eigenmodes and therefore suffer from the fact that the numbers of eigenmodes to deflate increases proportionally to the volume, i.e. the approach does not scale with the volume. 
Expected Results: 1) The replacement of explicit deflation of eigenmodes by deflation of approximate eigenmodes, given explicitly by a hierarchical representation like in multigrid methods. Here, we will build on recent results from aggregation based adaptive algebraic multigrid methods for the WilsonDirac operator. Instead of being proportional to the volume we expect the cost of the new approach to proportional to the logarithm of the volume. 2) The incorporation of novel, efficient and highly parallel techniques to approximate the (block) diagonal of the inverse of the operator, or its trace. The efficiency of the two approaches will be compared computationally and as far as possible, analytically. 
Planned secondment(s):
 TCD: 5 PMs, M6M10, training in algorithms
 EUROTECH: 4 PMs, M31M34, scaling and performance test
