Topics in Ultrascale Scientific Computing with Application

In this Thesis we focus on simulations of blood flow in three-dimensional patient-specific arterial networks. We employ high-order spectral/hp-element spatial discretization and con-centrate on computational efficiency in solving multi-million degrees of freedom (DOF) flow problems on petaflop computers. We develop new two-level domain decomposition method and multilevel communicating interface for ultra-parallel flow simulations. Specifically, at the coarse level the computational domain is subdivided into several big patches. Within each patch a spectral element discretization (fine level) is employed. New interface condi-tions for the Navier-Stokes equations are developed. The proposed numerical approach has been tested in arterial flow simulations with up to 147 arteries. Solution of 2.87B DOF problem was computed on 18,576 processors in less than one second at each time step. A scalable and fast parallel low-energy bases preconditioner (LEBP) in conjunction with coarse-space linear vertex solver is developed. We provide details on optimization, parallel performance and implementation of the coarse-space solver and show scalability of LEBP on thousands processors of the IBM BlueGene/L and the Cray XT3. An embarrassingly parallel but extremely efficient accelerator for iterative solver has been proposed. The ne