Algebraic Error Analysis for Mixed-Precision Multigrid Solvers

Mixed-Precision GPU-Multigrid Solvers with Strong Smoothers

• Sparse iterative linear solvers are the most important building block in (implicit) schemes for PDE problems • In FD, FV and FE discretisations • Lots of research on GPUs so far for Krylov subspace methods, ADI approaches and multigrid • But: Limited to simple preconditioners and smoothing operators •Numerically strong smoothers exhibit inherently sequential data dependencies (impossible to p...

Algebraic Multigrid Solvers for Complex-Valued Matrices

In the mathematical modeling of real-life applications, systems of equations with complex coefficients often arise. While many techniques of numerical linear algebra, e.g., Krylovsubspace methods, extend directly to the case of complex-valued matrices, some of the most effective preconditioning techniques and linear solvers are limited to the real-valued case. Here, we consider the extension of...

Analysis Tools for CFD Multigrid Solvers

Analysis tools are needed to guide the development and evaluate the performance of multigrid solvers for the fluid flow equations. Classical analysis tools, such as local mode analysis, often fail to accurately predict performance. Two-grid analysis tools, herein referred to as Idealized Coarse Grid and Idealized Relaxation iterations, have been developed and evaluated within a pilot multigrid ...

Detection of Strong Coupling in Algebraic Multigrid Solvers.

Comparative Performance Analysis of Coarse Solvers for Algebraic Multigrid on Multicore and Manycore Architectures

We study the performance of a two-level algebraic-multigrid algorithm, with a focus on the impact of the coarse-grid solver on performance. We consider two algorithms for solving the coarse-space systems: the preconditioned conjugate gradient method and a new robust HSSembedded low-rank sparse-factorization algorithm. Our test data comes from the SPE Comparative Solution Project for oil-reservo...