Lehel Banjai

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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(More)
In this paper we propose and analyze a new, fast method for the numerical solution of time domain boundary integral formulations of the wave equation. We employ Lubich’s convolution quadrature method for the time discretization and a Galerkin boundary element method for the spatial discretization. The coefficient matrix of the arising system of linear(More)
An error analysis of Runge-Kutta convolution quadrature is presented for a class of nonsectorial operators whose Laplace transform satisfies, besides the standard assumptions of analyticity in a half-plane Re s > σ0 and a polynomial bound O(s 1) there, the stronger polynomial bound O(s2) in convex sectors of the form | arg s| ≤ π/2 − θ < π/2 for θ > 0. The(More)
In this paper, we consider the numerical discretization of elliptic eigenvalue problems by Finite Element Methods and its solution by a multigrid method. From the general theory of finite element and multigrid methods, it is well known that the asymptotic convergence rates become visible only if the mesh width h is sufficiently small, h ≤ h0. We investigate(More)
In this paper we consider time-dependent electromagnetic scattering problems from conducting objects. We discretize the time-domain electric field integral equation using RungeKutta convolution quadrature in time and a Galerkin method in space. We analyze the involved operators in the Laplace domain and obtain convergence results for the fully discrete(More)
Crowding is an intrinsic problem of all numerical conformal mapping techniques. The distance between some of the prevertices of a Schwarz-Christoffel map to an elongated polygon is exponentially small in the aspect ratio of the elongation. We show that a simple change, no domain decomposition or change of canonical domain is needed, to the existing(More)
In this paper, we discuss the application of hierarchical matrix techniques to the solution of Helmholtz problems with large wave number κ in two dimensions. We consider the Brakhage-Werner integral formulation of the problem, discretised by the Galerkin boundary element method. The dense n×n Galerkin matrix arising from this approach is represented by a(More)