Sums of squares approximations in polynomial optimization: performance analysis and degree bounds
De Monique Laurent
Some advances in numerical algebraic geometry for computing real solutions
De Jon Hauenstein
De Andy Wathen
Apparaît dans la collection : Parallel Solution Methods for Systems Arising from PDEs / Méthodes parallèles pour la résolution de systèmes issus d'équations aux dérivées partielles
We present a novel approach to the solution of time-dependent PDEs via the so-called monolithic or all-at-once formulation. This approach will be explained for simple parabolic problems and its utility in the context of PDE constrained optimization problems will be elucidated. The underlying linear algebra includes circulant matrix approximations of Toeplitz-structured matrices and allows for effective parallel implementation. Simple computational results will be shown for the heat equation and the wave equation which indicate the potential as a parallel-in-time method. This is joint work with Elle McDonald (CSIRO, Australia), Jennifer Pestana (Strathclyde University, UK) and Anthony Goddard (Durham University, UK)