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- Lehel Banjai, Stefan A. Sauter
- SIAM J. Numerical Analysis
- 2007

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)

- Lehel Banjai, Stefan A. Sauter
- SIAM J. Numerical Analysis
- 2008

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)

- Lehel Banjai
- SIAM J. Scientific Computing
- 2010

- Lehel Banjai, Christian Lubich, Jens Markus Melenk
- Numerische Mathematik
- 2011

An error analysis of Runge-Kutta convolution quadrature is presented for a class of non-sectorial operators whose Laplace transform satisfies, besides the standard assumptions of ana-lyticity in a half-plane Re s > σ 0 and a polynomial bound O(s µ1) there, the stronger polynomial bound O(s µ2) in convex sectors of the form | arg s| ≤ π/2 − θ < π/2 for θ >… (More)

An error analysis is given for convolution quadratures based on strongly A-stable Runge-Kutta methods, for the non-sectorial case of a convolution kernel with a Laplace transform that is polynomially bounded in a half-plane. The order of approximation depends on the classical order and stage order of the Runge-Kutta method and on the growth exponent of the… (More)

- Lehel Banjai, Lloyd N. Trefethen
- SIAM J. Scientific Computing
- 2003

A method is presented for the computation of Schwarz–Christoffel maps to polygons with tens of thousands of vertices. Previously published algorithms have CPU time estimates of the order O(N 3) for the computation of a conformal map of a polygon with N vertices. This has been reduced to O(N log N) by the use of the fast multipole method and Davis's method… (More)

- Lehel Banjai
- 2005

A method for the computation of eigenfrequencies and eigenmodes of fractal drums is presented. The approach involves first mapping the unit disk to a polygon approximating the fractal and then solving a weighted eigenvalue problem on the unit disk by a spectral collocation method. The numerical computation of the complicated conformal mapping was made… (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)

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 ≤ h 0. We… (More)

- Jonas Ballani, Lehel Banjai, Stefan A. Sauter, Alexander Veit
- Numerische Mathematik
- 2013

In this paper we consider time-dependent electromagnetic scattering problems from conducting objects. We discretize the time-domain electric field integral equation using Runge-Kutta 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)