Multilevel Quasi Monte Carlo Methods for Elliptic PDEs with Random Field Coefficients via Fast White Noise Sampling

When solving partial differential equations (PDEs) with random fields as coefficients, the efficient sampling of field realizations can be challenging. In this paper we focus on fast Gaussian using quasi-random points in a finite element and multilevel quasi Monte Carlo (MLQMC) setting. Our method uses stochastic PDE (SPDE) approach Lindgren et al. combined new algorithm for white noise which is tailored to (ML)QMC. We express wavelet series expansion that divide into two parts. The first part sampled contains number terms order decaying importance ensure good (QMC) convergence. second correction term standard pseudo-random numbers. show how both performed linear time memory complexity mesh cells via supermesh construction, yielding an overall cost. Furthermore, our technique used enforce MLQMC coupling even case nonnested hierarchies. demonstrate efficacy numerical experiments.