summary:In this paper we study the $q$-version of the Partition of Unity Method for the Helmholtz equation. The method is obtained by employing the standard bilinear finite element basis on a mesh of quadrilaterals discretizing the domain as the Partition of Unity used to paste together local bases of special wave-functions employed at the mesh vertices. The main topic of the paper is the comparison of the performance of the method for two choices of local basis functions, namely a) plane-waves, and b) wave-bands. We establish the $q$-convergence of the method for the class of analytical solutions, with $q$ denoting the number of plane-waves or wave-bands employed at each vertex, for which we get better than exponential convergence for suf...
Includes bibliographical references (pages 59-62)Traditional plane wave based methods for solving wa...
The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary ...
The application of computational modelling to wave propagation problems is hindered by the dispersio...
summary:In this paper we study the $q$-version of the Partition of Unity Method for the Helmholtz eq...
In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces fo...
AbstractThere has been considerable attention given in recent years to the problem of extending fini...
Global radial basis function (RBF) collocation methods with inifinitely smooth basis functions for p...
Ebene Wellen lösen die homogene Helmholtz-Gleichung (lokal) und bieten daher eine gängige Wahl als T...
There has been considerable attention given in recent years to the problem of extending finite and b...
In comparison with low-order finite element methods (FEMs), the use of oscillatory basis functions h...
We present a wavenumber-explicit convergence analysis of the hp Finite Element Method applied to a c...
Die vorliegende Arbeit befasst sich mit drei großen Themenblöcken. Zu Beginn der Arbeit betrachten w...
The method of plane wave basis functions, a subset of the method of Partition of Unity, has previous...
Numerical solutions of the Helmholtz equation suffer from pollution effect especially for higher wav...
Some meshless methods have been applied to the numerical solution of boundary value problems involvi...
Includes bibliographical references (pages 59-62)Traditional plane wave based methods for solving wa...
The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary ...
The application of computational modelling to wave propagation problems is hindered by the dispersio...
summary:In this paper we study the $q$-version of the Partition of Unity Method for the Helmholtz eq...
In this paper, a generalized finite element method (GFEM) with optimal local approximation spaces fo...
AbstractThere has been considerable attention given in recent years to the problem of extending fini...
Global radial basis function (RBF) collocation methods with inifinitely smooth basis functions for p...
Ebene Wellen lösen die homogene Helmholtz-Gleichung (lokal) und bieten daher eine gängige Wahl als T...
There has been considerable attention given in recent years to the problem of extending finite and b...
In comparison with low-order finite element methods (FEMs), the use of oscillatory basis functions h...
We present a wavenumber-explicit convergence analysis of the hp Finite Element Method applied to a c...
Die vorliegende Arbeit befasst sich mit drei großen Themenblöcken. Zu Beginn der Arbeit betrachten w...
The method of plane wave basis functions, a subset of the method of Partition of Unity, has previous...
Numerical solutions of the Helmholtz equation suffer from pollution effect especially for higher wav...
Some meshless methods have been applied to the numerical solution of boundary value problems involvi...
Includes bibliographical references (pages 59-62)Traditional plane wave based methods for solving wa...
The Method of Fundamental Solutions (MFS) is a popular tool to solve Laplace and Helmholtz boundary ...
The application of computational modelling to wave propagation problems is hindered by the dispersio...