We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special recently developed parallelization technique to avoid communication bottleneck for the computation associated ...

An iterative solver based on the immersed interface method is proposed to solve the pressure in a two-fluid flow on a Cartesian grid. The iteration is constructed by introducing an unsteady term in the pressure Poisson equation. In each iteration step, a Helmholtz equation is solved on the Cartesian grid using FFT. The combination of the iteration and the immersed interface method enables the s...

One major challenge in applying the adjoint method to large industrial cases is the lack of robustness of the flow and adjoint solvers. Discrete adjoints transpose the Jacobian of the system of discretised equations exactly, and hence inherit the linear stability from the primal flow solver. Typically the linear stability properties of the iterative scheme of the flow solver is very well unders...

We discuss a parallel algorithm for the solution of large-scale generalized algebraic Riccati equations with dimension up to O(10). We survey the numerical algorithms underlying the implementation of the method, in particular, a Newton-type iterative solver for the generalized Riccati equation and an LR-ADI solver for the generalized Lyapunov equation. Experimental results on a cluster of Intel...

This paper analyzes and evaluates some novel latency hiding features of the KSR1 multiprocessor: prefetch and poststore instructions and automatic updates. As a case study, we analyze the performance of an iterative sparse solver which generates irregular communications. We show that automatic updates signiicantly reduce the amount of communication. Although prefetch and poststore instructions ...

We present numerical enhancements of a multiscale domain decomposition strategy based on a LaTIn solver and dedicated to the computation of the debounding in laminated composites. We show that the classical scale separation is irrelevant in the process zones, which results in a drop in the convergence rate of the strategy. We show that performing nonlinear subresolutions in the vicinity of the ...