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We consider several methods for generating initial guesses when iteratively solving sequences of linear systems, showing that they can be implemented efficiently in GPU-accelerated PDE solvers, specifically solvers for incompressible flow. We propose new initial guess methods based on stabilized polynomial extrapolation and compare them to the projection method of Fischer [15], showing that they are generally competitive with projection schemes despite requiring only half the storage and performing considerably less data movement and communication. Our implementations of these algorithms are freely available as part of the libParanumal collection of GPU-accelerated flow solvers.
The linear equations that arise in interior methods for constrained optimization are sparse symmetric indefinite and become extremely ill-conditioned as the interior method converges. These linear systems present a challenge for existing solver frame
In this paper, we present a class of finite volume schemes for incompressible flow problems. The unknowns are collocated at the center of the control volumes, and the stability of the schemes is obtained by adding to the mass balance stabilization te
We propose an efficient, accurate and robust implicit solver for the incompressible Navier-Stokes equations, based on a DG spatial discretization and on the TR-BDF2 method for time discretization. The effectiveness of the method is demonstrated in a
We develop and use a novel mixed-precision weighted essentially non-oscillatory (WENO) method for solving the Teukolsky equation, which arises when modeling perturbations of Kerr black holes. We show that WENO methods outperform higher-order finite-d
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits th