# 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

- MathematicsSIAM J. Sci. Comput.
- 2017

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 discretization of a stable time-domain integral equation for 3D acoustic scattering

- MathematicsJ. Comput. Phys.
- 2020

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

- MathematicsAdv. Comput. Math.
- 2014

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

- Computer ScienceSIAM J. Numer. Anal.
- 2008

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.

### A Nyström flavored Calderón Calculus of order three for two dimensional waves, time-harmonic and transient

- MathematicsComput. Math. Appl.
- 2014

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

- Mathematics
- 2015

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

- MathematicsProceedings of the Royal Society A
- 2019

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

- Mathematics
- 2013

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…

### A fully discrete Calderón calculus for the two-dimensional elastic wave equation

- MathematicsComput. Math. Appl.
- 2015

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

- Mathematics
- 2008

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…