• Corpus ID: 244102995

Nystr\"om methods for high-order CQ solutions of the wave equation in two dimensions

@inproceedings{Petropoulos2021NystromMF,
  title={Nystr\"om methods for high-order CQ solutions of the wave equation in two dimensions},
  author={Peter P. Petropoulos and Catalin Turc and Erli Wind-andersen},
  year={2021}
}
We investigate high-order Convolution Quadratures methods for the solution of the wave equation in unbounded domains in two dimensions that rely on Nyström discretizations for the solution of the ensemble of associated Laplace domain modified Helmholtz problems. We consider two classes of CQ discretizations, one based on linear multistep methods and the other based on Runge-Kutta methods, in conjunction with Nyström discretizations based on Alpert and QBX quadratures of Boundary Integral… 

References

SHOWING 1-10 OF 35 REFERENCES

Overresolving in the Laplace Domain for Convolution Quadrature Methods

Techniques from complex approximation theory are used to analyse the error of the CQ approximation of the underlying time-stepping rule when overresolving in the Laplace domain and show that the performance is intimately linked to the location of the poles of the solution operator.

High-order accurate methods for Nyström discretization of integral equations on smooth curves in the plane

This work describes the construction of four different quadratures which handle logarithmically-singular kernels, and compares in numerical experiments the convergence of the four schemes in various settings, including low- and high-frequency planar Helmholtz problems, and 3D axisymmetric Laplace problems.

Rapid Solution of the Wave Equation in Unbounded Domains

A new, fast method is proposed for the numerical solution of time domain boundary integral formulations of the wave equation using Lubich's convolution quadrature method and a Galerkin boundary element method for the spatial discretization of Helmholtz equations with complex wave numbers.

Well-posed boundary integral equation formulations and Nystr\"om discretizations for the solution of Helmholtz transmission problems in two-dimensional Lipschitz domains

We present a comparison between the performance of solvers based on Nystrom discretizations of several well-posed boundary integral equation formulations of Helmholtz transmission problems in

Convolution quadrature methods for time-domain scattering from unbounded penetrable interfaces

A high-order Nyström method based on Alpert's quadrature rules is used here, and a variety of CQ schemes and numerical examples, including wave propagation in open waveguides as well as scattering from multiple layered media, demonstrate the capabilities of the proposed approach.

Wave-number estimates for regularized combined field boundary integral operators in acoustic scattering problems with Neumann boundary conditions

We study the coercivity properties and the norm dependence on the wavenumber k of certain regularized combined field boundary integral operators that we recently introduced for the solution of two

Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations II

In this paper, we develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in

Second‐kind integral solvers for TE and TM problems of diffraction by open arcs

We present a novel approach for the numerical solution of problems of diffraction by open arcs in two dimensional space. Our methodology relies on composition of weighted versions of the classical