A robust adaptive algebraic multigrid linear solver for structural mechanics

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.Comment: 50 pages, 16 figures, submitted to CMAM

Motion Estimation and Compensation in Automotive MIMO SAR

With the advent of self-driving vehicles, autonomous driving systems will have to rely on a vast number of heterogeneous sensors to perform dynamic perception of the surrounding environment. Synthetic Aperture Radar (SAR) systems increase the resolution of conventional mass-market radars by exploiting the vehicle's ego-motion, requiring a very accurate knowledge of the trajectory, usually not compatible with automotive-grade navigation systems. In this regard, this paper deals with the analysis, estimation and compensation of trajectory estimation errors in automotive SAR systems, proposing a complete residual motion estimation and compensation workflow. We start by defining the geometry of the acquisition and the basic processing steps of Multiple-Input Multiple-Output (MIMO) SAR systems. Then, we analytically derive the effects of typical motion errors in automotive SAR imaging. Based on the derived models, the procedure is detailed, outlining the guidelines for its practical implementation. We show the effectiveness of the proposed technique by means of experimental data gathered by a 77 GHz radar mounted in a forward looking configuration.Comment: 14 page