Convergence analysis of two finite element methods for the modified Maxwell's Steklov eigenvalue problem

The modified Maxwell's Steklov eigenvalue problem is a new problem arising from the study of inverse electromagnetic scattering problems. In this paper, we investigate two finite element methods for this problem and perform the convergence analysis. Moreover, the monotonic convergence of the discrete eigenvalues computed by one of the methods is analyzed.

General Lyapunov-Based Iterative Algorithm for Linear Quadratic Regulator Problem of Stochastic Systems with Markovian Jump

This paper investigates the linear quadratic regulator(LQR) problem of linear stochastic systems with Markovian jump. Firstly, two iterative algorithms are proposed for solving the corresponding coupled algebraic Riccati equa- tions (CAREs) based on the general-type Lyapunov equation derived from linear stochastic systems. It is verified that the second algorithm adding an adjustable factor converges faster than the first one without it. Secondly, a monotonic convergence theorem is established for the proposed iterative algorithms under certain initial conditions. In the end, a numerical example is given to verify the efficiency of the proposed algorithms.

General Lyapunov-Based Iterative Algorithm for Linear Quadratic Regulator Problem of Stochastic Systems with Markovian Jump

This paper investigates the linear quadratic regulator(LQR) problem of linear stochastic systems with Markovian jump. Firstly, two iterative algorithms are proposed for solving the corresponding coupled algebraic Riccati equa- tions (CAREs) based on the general-type Lyapunov equation derived from linear stochastic systems. It is verified that the second algorithm adding an adjustable factor converges faster than the first one without it. Secondly, a monotonic convergence theorem is established for the proposed iterative algorithms under certain initial conditions. In the end, a numerical example is given to verify the efficiency of the proposed algorithms.

Computationally efficient source grid selection and source interpolation in computational aeroacoustics applied to an axial fan.

The noise generation of an axial fan is mainly caused by flow-induced noise and can therefore be extracted from its aeroacoustics. To do so, a hybrid approach separating flow and acoustics is well suited due to its low Mach number. Such a computationally efficient hybrid workflow requires a robust conservative mesh-to-mesh transformation of the acoustic sources as well as a suitable mesh refinement to guarantee good convergence behavior. This contribution focuses on the mesh-to-mesh transformation, comparing two interpolation algorithms of different complexity towards the applicability to the aeroacoustic computation of an axial fan. The basic cell-centroid approach is generally suited for fine computational acoustic (CA) meshes and low phase shift, while the more complex cut-volume method generally yields better results for coarse acoustic meshes. While the cell-centroid interpolation scheme produces source artifacts inside the propagation domain, a grid study using the grid convergence index shows monotonic convergence behavior for both interpolation methods. By selection of a proper size for the source grid and source interpolation algorithm, the computational effort of the experimentally validated simulation model could be reduced by a factor 4.06.

Discretization Error Estimation in Subsonic, Transonic and Supersonic Flows of an Inviscid Fluid Over a Bump

This paper presents a solution verification exercise for the simulation of subsonic, transonic and supersonic flows of an inviscid fluid over a circular arc (bump). Numerical simulations are performed with a pressure-based, single-phase compressible flow solver. Sets of geometrically similar grids covering a wide range of refinement ratios have been generated. The goal of these grids is twofold: obtain a reference solution from power series expansion fits applied to the finest grids; check the numerical uncertainties obtained from coarse grids that do not guarantee monotonic convergence of the quantities of interest. The results show that even with very fine grids it is not straightforward to define a reference solution from power series expansions. The level of discretization errors required to obtain reliable reference solutions implies iterative errors reduced to machine accuracy, which may be extremely time consuming even in two-dimensional inviscid flows. Quantitative assessment of the estimated uncertainties for coarse grids depends on the selected reference solution.

Behavior of the iterative ensemble-based variational method in nonlinear problems

The behavior of the iterative ensemble-based data assimilation algorithm is discussed. The ensemble-based method for variational data assimilation problems, referred to as the 4D ensemble variational method (4DEnVar), is a useful tool for data assimilation problems. Although the 4DEnVar is derived based on a linear approximation, highly uncertain problems, in which system nonlinearity is significant, are solved by applying this method iteratively. However, the ensemble-based methods basically seek the solution within a lower-dimensional subspace spanned by the ensemble members. It is not necessarily trivial how high-dimensional problems can be solved with the ensemble-based algorithm which employs the lower-dimensional approximation based on the ensemble. In the present study, an ensemble-based iterative algorithm is reformulated to allow us to analyze its behavior in high-dimensional nonlinear problems. The conditions for monotonic convergence to a local maximum of the objective function are discussed in a high-dimensional context. It is shown that the ensemble-based algorithm can solve high-dimensional problems by distributing the ensemble in different subspace at each iteration. The findings as the results of the present study were also experimentally supported.

Robust Iterative Learning Control for Interval Linear Systems

Many forms of system uncertainty result in interval description of linear systems, and numerically efficient design methods for the computation of robust iterative learning controllers with good learning transients for these systems are lacking. Using a Lyapunov framework, two design procedures that ensure robust convergence of the tracking error to zero with good learning transients are described in this study. Both methods are validated numerically for an application of position control, and robust and monotonic convergence of the tracking error to zero is demonstrated.

Optimization for L1-Norm Error Fitting via Data Aggregation

We propose a data aggregation-based algorithm with monotonic convergence to a global optimum for a generalized version of the L1-norm error fitting model with an assumption of the fitting function. The proposed algorithm generalizes the recent algorithm in the literature, aggregate and iterative disaggregate (AID), which selectively solves three specific L1-norm error fitting problems. With the proposed algorithm, any L1-norm error fitting model can be solved optimally if it follows the form of the L1-norm error fitting problem and if the fitting function satisfies the assumption. The proposed algorithm can also solve multidimensional fitting problems with arbitrary constraints on the fitting coefficients matrix. The generalized problem includes popular models, such as regression and the orthogonal Procrustes problem. The results of the computational experiment show that the proposed algorithms are faster than the state-of-the-art benchmarks for L1-norm regression subset selection and L1-norm regression over a sphere. Furthermore, the relative performance of the proposed algorithm improves as data size increases.