A modified QP-free feasible method

AbstractIn this paper, we presented a modified QP-free filter method based on a new piecewise linear NCP functions. In contrast with the existing QP-free methods, each iteration in this algorithm only needs to solve systems of linear equations which are derived from the equality part in the KKT first order optimality conditions. Its global convergence and local superlinear convergence are obtained under mild conditions

Optimization and Applications

Proceedings of a workshop devoted to optimization problems, their theory and resolution, and above all applications of them. The topics covered existence and stability of solutions; design, analysis, development and implementation of algorithms; applications in mechanics, telecommunications, medicine, operations research

An idealised fluid model of Numerical Weather Prediction: dynamics and data assimilation

The dynamics of the atmosphere span a tremendous range of spatial and temporal scales which presents a great challenge to those who seek to forecast the weather. To aid understanding of and facilitate research into such complex physical systems, `idealised' models can be developed that embody essential characteristics of these systems. This thesis concerns the development of an idealised fluid model of convective-scale Numerical Weather Prediction (NWP) and its use in inexpensive data assimilation (DA) experiments. The model modifies the rotating shallow water equations to include some simplified dynamics of cumulus convection and associated precipitation, extending the model of Wuersch and Craig (2014). Despite the non-trivial modifications to the parent equations, it is shown that the model remains hyperbolic in character and can be integrated accordingly using a discontinuous Galerkin finite element method for nonconservative hyperbolic systems of partial differential equations. Combined with methods to ensure well-balancedness and non-negativity, the resulting numerical solver is novel, efficient, and robust. Classical numerical experiments in shallow water theory, based on the Rossby geostrophic adjustment problem and non-rotating flow over topography, elucidate the model's distinctive dynamics, including the disruption of large-scale balanced flows and other features of convecting and precipitating weather systems. When using such intermediate-complexity models for DA research, it is important to justify their relevance in the context of NWP. A well-tuned observing system and filter configuration is achieved using the ensemble Kalman filter that adequately estimates the forecast error and has an average observational influence similar to NWP. Furthermore, the resulting error-doubling time statistics reflect those of convection-permitting models in a cycled forecast-assimilation system, further demonstrating the model's suitability for conducting DA experiments in the presence of convection and precipitation. In particular, the numerical solver arising from this research provides a useful tool to the community and facilitates other studies in the field of convective-scale DA research

A generic interior-point framework for nonsmooth and complementarity constrained nonlinear optimization

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Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS

In this article we present a noise reduction method (msPOAS) for multi-shell diffusion-weighted magnetic resonance data. To our knowledge, this is the first smoothing method which allows simultaneous smoothing of all q-shells. It is applied directly to the diffusion weighted data and consequently allows subsequent analysis by any model. Due to its adaptivity, the procedure avoids blurring of the inherent structures and preserves discontinuities. MsPOAS extends the recently developed position-orientation adaptive smoothing (POAS) procedure to multi-shell experiments. At the same time it considerably simplifies and accelerates the calculations. The behavior of the algorithm msPOAS is evaluated on diffusion-weighted data measured on a single shell and on multiple shells

Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS

In this article we present a noise reduction method (msPOAS) for multi-shell diffusion-weighted magnetic resonance data. To our knowledge, this is the first smoothing method which allows simultaneous smoothing of all q-shells. It is applied directly to the diffusion weighted data and consequently allows subsequent analysis by any model. Due to its adaptivity, the procedure avoids blurring of the inherent structures and preserves discontinuities. MsPOAS extends the recently developed position-orientation adaptive smoothing (POAS) procedure to multi-shell experiments. At the same time it considerably simplifies and accelerates the calculations. The behavior of the algorithm msPOAS is evaluated on diffusion-weighted data measured on a single shell and on multiple shells

Adaptive smoothing of multi-shell diffusion-weighted magnetic resonance data by msPOAS

In this article we present a noise reduction method (msPOAS) for multi-shell diffusionweighted magnetic resonance data. To our knowledge, this is the first smoothing method which allows simultaneous smoothing of all q-shells. It is applied directly to the diffusion weighted data and consequently allows subsequent analysis by any model. Due to its adaptivity, the procedure avoids blurring of the inherent structures and preserves discontinuities. MsPOAS extends the recently developed positionorientation adaptive smoothing (POAS) procedure to multi-shell experiments. At the same time it considerably simplifies and accelerates the calculations. The behavior of the algorithm msPOAS is evaluated on diffusion-weighted data measured on a single shell and on multiple shells

Development of Shape-Optimization Tools for the Aerodynamic Design of Turbomachinery Blades

The aim of this work is to develop an automated tool for the optimization of turbomachinery blades founded on an evolutionary strategy. This optimization scheme will serve to deal with supersonic blades cascades for application to Organic Rankine Cycle (ORC) turbines. The blade geometry is defined using parameterization techniques based on B-Splines curves, that allow to have a local control of the shape. The location in space of the control points of the B-Spline curve define the design variables of the optimization problem. In the present work, the performance of the blade shape is assessed by means of fully-turbulent flow simulations performed with a CFD package, in which a look-up table method is applied to ensure an accurate thermodynamic treatment. The solver is set along with the optimization tool to determine the optimal shape of the blade. As only blade-to-blade effects are of interest in this study, quasi-3D calculations are performed, and a single-objective evolutionary strategy is applied to the optimization. As a result, a non-intrusive tool, with no need for gradients definition, is developed. The computational cost is reduced by the use of surrogate models. A Gaussian interpolation scheme (Kriging model) is applied for the estimated n-dimensional function, and a surrogate-based local optimization strategy is proved to yield an accurate way for optimization. In particular, the present optimization scheme has been applied to the re-design of a supersonic stator cascade of an axial-flow turbine. In this design exercise very strong shock waves are generated in the rear blade suction side and shock-boundary layer interaction mechanisms occur. A significant efficiency improvement as a consequence of a more uniform flow at the blade outlet section of the stator is achieved. This is also expected to provide beneficial effects on the design of a subsequent downstream rotor. The method provides an improvement to gradient-based methods and an optimized blade geometry is easily achieved using the genetic algorithm