Convolution Quadrature for Wave Simulations

Hassell, Matthew E.; Sayas, Francisco–Javier

doi:10.48550/arxiv.1407.0345

Cited by 5 publications

(10 citation statements)

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“…An underlying ODE solver is used to carry out the time discretization, which can be any A-stable linear multistep method or an implicit Runge-Kutta method. For a comprehensive introduction to the algorithmic aspects of CQ, see [11,18]. We present here a simple example to demonstrate the method.…”

Section: Full Discretizationmentioning

confidence: 99%

A fully discrete BEM–FEM scheme for transient acoustic waves

Hassell

Sayas

2016

Computer Methods in Applied Mechanics and Engineering

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We study a symmetric BEM-FEM coupling scheme for the scattering of transient acoustic waves by bounded inhomogeneous anisotropic obstacles in a homogeneous field. An incident wave in free space interacts with the obstacles and produces a combination of transmission and scattering. The transmitted part of the wave is discretized in space by finite elements while the scattered wave is reduced to two fields defined on the boundary of the obstacles and is discretized in space with boundary elements. We choose a coupling formulation that leads to a symmetric system of integro-differential equations. The retarded boundary integral equations are discretized in time by Convolution Quadrature, and the interior field is discretized in time with the trapezoidal rule. We show that the scattering problem generates a C 0 group of isometries in a Hilbert space, and use associated estimates to derive stability and convergence results. We provide numerical experiments and simulations to validate our results and demonstrate the flexibility of the method.

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Section: Full Discretizationmentioning

confidence: 99%

A fully discrete BEM–FEM scheme for transient acoustic waves

Hassell

Sayas

2016

Computer Methods in Applied Mechanics and Engineering

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“…For theoretical aspects of multistep CQ methods applied to wave propagation, the reader is referred to [18,16,24]. Practical aspects on the implementation of CQ can be found in [4,5,14]. A concise explanation on how to use CQ for an acoustic wave propagation problem discretized with a method that is similar to the one in this paper is given in [10].…”

Section: Experiments In the Time Domainmentioning

confidence: 99%

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

Domínguez¹,

Sánchez-Vizuet²,

Sayas³

2015

Computers & Mathematics with Applications

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In this paper we present a full discretization of the layer potentials and boundary integral operators for the elastic wave equation on a parametrizable smooth closed curve in the plane. The method can be understood as a non-conforming Petrov-Galerkin discretization, with a very precise choice of testing functions by symmetrically combining elements on two staggered grids, and using a look-around quadrature formula. Unlike in the acoustic counterpart of this work, the kernel of the elastic double layer operator includes a periodic Hilbert transform that requires a particular choice of the mixing parameters. We give mathematical justification of this fact. Finally, we test the method on some frequency domain and time domain problems, and demonstrate its applicability on smooth open arcs.

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“…A modern introduction to computational uses of CQ for wave propagation problems is given in [8]. Algorithmic details and several possible interpretations of CQ can be found in [18]. In this section we will follow the plan developed in [26,Section 10.3], based on [5, Section 6].…”

Section: Long Term Analysis In Free Spacementioning

confidence: 99%

“…For time-stepping we have used a simple BDF2-based Convolution Quadrature method: the analysis for the trapezoidal rule discretization follows very similar arguments and can be easily adapted from what appears in Section 6 of this work and [5, Section 6]. Higher order much less dispersive discretizations are easily attainable using RK-based CQ methods [4,7,8,18]. In that case the analysis relies entirely on Laplace domain estimates and the behavior of the bounds with respect to the time variable is still unclear.…”

Section: Introductionmentioning

confidence: 99%

The Costabel-Stephan system of boundary integral equations in the time domain

Qiu

Sayas

2015

Math. Comp.

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In this paper we formulate a transmission problem for the transient acoustic wave equation as a system of retarded boundary integral equations. We then analyse a fully discrete method using a general Galerkin semidiscretization-in-space and Convolution Quadrature in time. All proofs are developed using recent techniques based on the theory of evolution equations. Some numerical experiments are provided.

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Convolution Quadrature for Wave Simulations

Cited by 5 publications

References 0 publications

A fully discrete BEM–FEM scheme for transient acoustic waves

A fully discrete BEM–FEM scheme for transient acoustic waves

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

The Costabel-Stephan system of boundary integral equations in the time domain

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