12 research outputs found
Fourier Method for Approximating Eigenvalues of Indefinite Stekloff Operator
We introduce an efficient method for computing the Stekloff eigenvalues
associated with the Helmholtz equation. In general, this eigenvalue problem
requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary
condition repeatedly. We propose solving the related constant coefficient
Helmholtz equation with Fast Fourier Transform (FFT) based on carefully
designed extensions and restrictions of the equation. The proposed Fourier
method, combined with proper eigensolver, results in an efficient and clear
approach for computing the Stekloff eigenvalues.Comment: 12 pages, 4 figure
On the validity of the local Fourier analysis
Local Fourier analysis (LFA) is a useful tool in predicting the convergence
factors of geometric multigrid methods (GMG). As is well known, on rectangular
domains with periodic boundary conditions this analysis gives the exact
convergence factors of such methods. In this work, using the Fourier method, we
extend these results by proving that such analysis yields the exact convergence
factors for a wider class of problems
Recommended from our members
Low Eigenvalues of Laplace and Schrödinger Operators
This workshop brought together researchers interested in eigenvalue problems for Laplace and Schršdinger operators. The main topics o of discussions and investigations covered Dirichlet and Neumann eigenvalue problems, inequalities for the spectral gap, isoperimertic problems and sharp LiebâThirring type inequalities. The focus included not only the analytic and geometric sides of the problems, but also related probabilistic and computational aspects
International Congress of Mathematicians: 2022 July 6â14: Proceedings of the ICM 2022
Following the long and illustrious tradition of the International Congress of Mathematicians, these proceedings include contributions based on the invited talks that were presented at the Congress in 2022.
Published with the support of the International Mathematical Union and edited by Dmitry Beliaev and Stanislav Smirnov, these seven volumes present the most important developments in all fields of mathematics and its applications in the past four years. In particular, they include laudations and presentations of the 2022 Fields Medal winners and of the other prestigious prizes awarded at the Congress.
The proceedings of the International Congress of Mathematicians provide an authoritative documentation of contemporary research in all branches of mathematics, and are an indispensable part of every mathematical library
Mathematical and Numerical Aspects of Dynamical System Analysis
From Preface: This is the fourteenth time when the conference âDynamical Systems: Theory and Applicationsâ gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled âDynamical Systemsâ with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled âDynamical Systems in Theoretical Perspectiveâ and âDynamical Systems in Applicationsâ
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal