Fast Parallel Solver for the Space-time IgA-DG Discretization of the Diffusion Equation

We consider the space-time discretization of the diffusion equation, using an isogeometric analysis (IgA) approximation in space and a discontinuous Galerkin (DG) approximation in time. Drawing inspiration from a former spectral analysis, we propose for the resulting space-time linear system a multigrid preconditioned GMRES method, which combines a preconditioned GMRES with a standard multigrid acting only in space. The performance of the proposed solver is illustrated through numerical experiments, which show its competitiveness in terms of iteration count, run-time and parallel scaling.

MADAM: a parallel exact solver for max-cut based on semidefinite programming and ADMM

We present , a parallel semidefinite-based exact solver for Max-Cut, a problem of finding the cut with the maximum weight in a given graph. The algorithm uses the branch and bound paradigm that applies the alternating direction method of multipliers as the bounding routine to solve the basic semidefinite relaxation strengthened by a subset of hypermetric inequalities. The benefit of the new approach is a less computationally expensive update rule for the dual variable with respect to the inequality constraints. We provide a theoretical convergence of the algorithm as well as extensive computational experiments with this method, to show that our algorithm outperforms state-of-the-art approaches. Furthermore, by combining algorithmic ingredients from the serial algorithm, we develop an efficient distributed parallel solver based on MPI.

PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS

Recently, we developed a numerical approach for the simulation of detonation waves on fully unstructured grids and applied it to the numerical study of the mechanisms of detonation initiation in multifocusing systems. Current work is devoted to further development of our numerical approach, namely, parallelization of the numerical scheme and introduction of more comprehensive detailed chemical kinetics scheme.