Matrix-Free High-Performance Saddle-Point Solvers for High-Order Problems in H (div)

This work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in . The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have applications in radiation diffusion and porous media flow problems, among others. Using the interpolation–histopolation basis (cf. [W. Pazner, T. Kolev, and C. R. Dohrmann, SIAM J. Sci. Comput., 45 (2023), pp. A675–A702]), efficient matrix-free preconditioners can be constructed for the -block and Schur complement of the block system. With these approximations, block-preconditioned MINRES converges in a number of iterations that is independent of the mesh size and polynomial degree. The approximate Schur complement takes the form of an M-matrix graph Laplacian and therefore can be well-preconditioned by highly scalable algebraic multigrid methods. High-performance GPU-accelerated algorithms for all components of the solution algorithm are developed, discussed, and benchmarked. Numerical results are presented on a number of challenging test cases, including the “crooked pipe” grad-div problem, the SPE10 reservoir modeling benchmark problem, and a nonlinear radiation diffusion test case

Introduction to “The social theories of classical political economy and modern economic policy”

This is the first-ever English translation of an 1891 essay by Carl Menger published in the most important newspaper of the Habsburg Empire, the Neue Freie Presse. Menger writes the piece as a defense of classical political economy in general and of Adam Smith in particular, focusing on misinterpretations of Smith’s work by the Younger Historical School in Germany. The essay reveals that Menger saw himself as working in a liberal tradition going back to Smith and classical political economy, rather than as a marginalist revolutionary who broke with classical political economy. It is a rare instance where Menger, holding the chair of economic theory at the University of Vienna, publicly expresses recommendations on economic policy. The essay represents Smith and the other classical political economists as socially motivated scholars concerned with just reforms to benefit ordinary people. Menger argues that the classical political economists were inclined toward liberal reforms but were by no means rigid exponents of laissez-faire. The essay is preceded here by an introduction authored by the translators Erwin Dekker and Stefan Kolev

Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is positive definite (or positive semidefinite). We state a characterization in the form of equivalent conditions, and also propose some computationally cheap sufficient\,/\,necessary conditions. Our results extend the classical results on positive (semi-)definiteness of interval matrices. They may be useful for checking convexity or non-convexity in global optimization methods based on branch and bound framework and using interval techniques

PD pattern recognition using ANFIS

An application of an adaptive neuro-fuzzy inference system (ANFIS) has been investigated for partial discharge (PD) pattern recognition. The proposed classifier was used to discriminate between PD patterns occurring in internal voids. Three different void shapes were considered in this work, namely flat, square and narrow. Initially, the input feature vector used for classification was based on 15 statistical parameters. The discrimination capabilities of each feature were assessed by applying discriminant analysis. This analysis suggested that some of the features possess much higher discriminatory power than the others. As a result, a simplified classifier with reduced feature vector has been obtained. The results demonstrate the importance in identifying and removing redundancy in the input feature vector for reliable PD identification

Identification of temperature profile and heat transfer on a dielectric membrane for gas sensors by `COSMOS' program simulation

The application of commercial 3-D software `COSMOS' for the design and thermal analysis of the low power consumption test structures with dielectric membrane for gas microsensors is presented. Within this work, the simulation provides the estimation of the temperature profile on the active area and the whole membrane including the four bridges and the heating efficiency in the temperature range 20-500 °C. Unravelling of the heat loss mechanisms in terms of radiation, convection, conduction by air and solid materials during heat transfer on the dielectric membrane is reported for the first time as a mean to evaluate by 3-D simulation the contribution of technological processes and lay-out design to the total heat losses

The Degasperis-Procesi equation as a non-metric Euler equation

In this paper we present a geometric interpretation of the periodic Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric linear connection on the diffeomorphism group of the circle. We also show that for any evolution in the family of $b$-equations there is neither gain nor loss of the spatial regularity of solutions. This in turn allows us to view the Degasperis-Procesi and the Camassa-Holm equation as an ODE on the Fr\'echet space of all smooth functions on the circle.Comment: 17 page