Some properties of layer potentials and boundary integral operators for the wave equation

@article{Domnguez2011SomePO,
  title={Some properties of layer potentials and boundary integral operators for the wave equation},
  author={V{\'i}ctor Dom{\'i}nguez and Francisco-Javier Sayas},
  journal={arXiv: Analysis of PDEs},
  year={2011}
}
In this work we establish some new estimates for layer potentials of the acoustic wave equation in the time domain, and for their associated retarded integral operators. These estimates are proven using time-domain estimates based on theory of evolution equations and improve known estimates that use the Laplace transform. 
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References

SHOWING 1-10 OF 19 REFERENCES

Energy estimates for Galerkin semidiscretizations of time domain boundary integral equations

  • F. Sayas
  • Mathematics
    Numerische Mathematik
  • 2013
A battery of results related to how Galerkin semidiscretization in space affects some formulations of wave scattering and propagation problems when retarded boundary integral equations are used are presented.

Theoretical aspects of the application of convolution quadrature to scattering of acoustic waves

  • Antonio R. LalienaF. Sayas
  • Mathematics
    Numerische Mathematik
  • 2009
This paper proposes a new systematic way of dealing with the numerical approximation of the scattering of acoustic waves in two or three dimensions by penetrable non-homogeneous obstacles using convolution quadrature techniques for the time variable and coupled boundary element method/finite element method for the space variable.

On the multistep time discretization of linear\newline initial-boundary value problems and their boundary integral equations

Summary.Convergence estimates in terms of the data are shown for multistep methods applied to non-homogeneous linear initial-boundary value problems. Similar error bounds are derived for a new class…

Strongly Elliptic Systems and Boundary Integral Equations

Introduction 1. Abstract linear equations 2. Sobolev spaces 3. Strongly elliptic systems 4. Homogeneous distributions 5. Surface potentials 6. Boundary integral equations 7. The Laplace equation 8.…

Boundary Integral Operators on Lipschitz Domains: Elementary Results

The simple and double layer potentials for second order linear strongly elliptic differential operators on Lipschitz domains are studied and it is shown that in a certain range of Sobolev spaces, r...

An error analysis of Runge–Kutta convolution quadrature

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…

Runge–Kutta convolution quadrature for operators arising in wave propagation

Numerical examples from acoustic scattering show that the theory describes accurately the convergence behaviour of Runge–Kutta convolution quadrature for this class of applications.

Finite Elements: Theory, Fast Solvers, and Applications in Elasticity Theory

This chapter discusses methods for conforming finite elements in solid mechanics using the conjugate gradient method and its applications in medicine and engineering.

Formulation variationnelle espace‐temps pour le calcul par potentiel retardé de la diffraction d'une onde acoustique (I)

We give here a space-time variational formula to the problem of the transient acoustic scattering by a free (pressure release) surface, using the retarded potential technique. From this formula, we…

Formulation variationnelle pour le calcul de la diffraction d'une onde acoustique par une surface rigide

This work is a continuation of our paper Formulation variationnelle espace-temps pour le calcul par potentiel retarde de la diffraction d'une onde acoustique . We give a space·time variational…