We examine how the wavenumber influences the compression in a wavelet boundary element method for the Helmholtz equation. We show that for wavelets with high vanishing moments the number of nonzeros in the resulting compressed matrix is approximately proportional to the square of the wavenumber. When the wavenumber is fixed, the wavelet boundary element method has optimal complexity with respec...

AbstructIn basic electrostatics, the formula for the capacitance of parallel-plate capacitors is derived, for the case that the spacing between the electrodes is very small compared to the length or width of the plates. However, when the separation is wide, the formula for very small separation does not provide accurate results. In our previously published papers, we use the boundary element me...

The signal induced by an electron on a pickup strip has been calculated in a RPC used in INO calorimeter [1] following Ramo’s theorem [2]. An accurate estimation of weighting field has been obtained using a nearly exact Boundary Element Method (neBEM) solver [3] while the electron velocity from the real field values. The calculation has shown a growth and subsequent fall of pickup signal with d...

In the direct boundary integral equation method, boundary-value problems are reduced to integral equations by an application of Green’s theorem to the unknown function and a fundamental solution (Green’s function). Discretization of the integral equation then leads to a boundary element method. This approach was pioneered by Jaswon and his students in the early 1960s. Jaswon’s work is reviewed ...

The convergence analysis of multigrid methods for boundary element equations arising from negative-order pseudo-differential operators is quite different from the usual finite element multigrid analysis for elliptic partial differential equations. In this paper, we study the convergence of geometric multigrid methods for solving large-scale, data-sparse boundary element equations arising from t...

Recently, a refined finite element analysis for highly indefinite Helmholtz problems was introduced by the second author. We generalise the analysis to the Galerkin method applied to an abstract, highly indefinite variational problem. In the refined analysis, the condition for stability and a quasi-optimal error estimate is expressed in terms of approximation properties T (S) ≈ S and T (u + S) ...

An efficient method to solve time harmonic Maxwell’s equations in exterior domain for high frequencies is obtained by using the integral formulation of Després combined with a coupling method (MLFMD) based on the Microlocal Discretization method (MD) and the Multi-Level Fast Multipole Method (MLFMM) [1]. In this paper, we consider curved finite elements of higher order in the MLFMD method. More...

This paper is devoted to the fast solution of interface concentrated finite element equations. The interface concentrated finite element schemes are constructed on the basis of a non-overlapping domain decomposition where a conforming boundary concentrated finite element approximation is used in every subdomain. Similar to data-sparse boundary element domain decomposition methods the total numb...

This paper presents three new coupling methods for interior penalty discontinuous Galerkin finite element methods and boundary element methods. The new methods allow one to use discontinuous basis functions on the interface between the subdomains represented by the finite element and boundary element methods. This feature is particularly important when discontinuous Galerkin finite element meth...