High-order FEM–BEM computer models for wave propagation in unbounded and heterogeneous media: Application to time-harmonic acoustic horn problem

Ganesh, M.; Morgenstern, Charles

doi:10.1016/j.cam.2016.02.024

Cited by 23 publications

(21 citation statements)

References 12 publications

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“…The coupling of FE and boundary integral or boundary element methods through a combined variational problem has been applied to solving unbounded exterior problems, e.g. Poisson [16,17], Stokes [18,19], and wave scattering [20,21]. In contrast, the method of [22] separates the solution into two additive parts: a finite element solution found on the regular mesh, and an integral equation solution defined by the boundary of the actual domain.…”

Section: ωωmentioning

confidence: 99%

High-order finite element–integral equation coupling on embedded meshes

Beams¹,

Klöckner²,

Olson³

2018

Journal of Computational Physics

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This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or inhomogeneous jump conditions without modification and retains high-order convergence close to the embedded interface. We present finite element-integral equation (FE-IE) formulations for interior, exterior, and interface problems. The treatments of the exterior and interface problems are new. The resulting linear systems are solved through an iterative approach exploiting the second-kind nature of the IE operator combined with algebraic multigrid preconditioning for the FE part. Assuming smooth continuations of coefficients and right-hand-side data, we show error analysis supporting high-order accuracy. Numerical evidence further supports our claims of efficiency and high-order accuracy for smooth data.

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Section: ωωmentioning

confidence: 99%

High-order finite element–integral equation coupling on embedded meshes

Beams¹,

Klöckner²,

Olson³

2018

Journal of Computational Physics

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“…Such complicated-structured coupled large-scale systems can be avoided, for the Helmholtz PDE interior and exterior problems, using the approach proposed in [35] and recently further explored in [24] using high-order elements for a class of applications with complex heterogeneous structures. The FEM-BEM algorithms in [24,35] are based on the idea of using a non-overlapping smooth interface to couple the interior and exterior solutions. As described in [24,Section 6], there are several open mathematical analysis problems remain to be solved in the coupling and FEM-BEM framework of [24,35].…”

Section: Introductionmentioning

confidence: 99%

“…The FEM-BEM algorithms in [24,35] are based on the idea of using a non-overlapping smooth interface to couple the interior and exterior solutions. As described in [24,Section 6], there are several open mathematical analysis problems remain to be solved in the coupling and FEM-BEM framework of [24,35].…”

Section: Introductionmentioning

confidence: 99%

“…The choice of smooth interface in the FEM-BEM algorithms of [24,35] is crucial because the methods require solving several interior and exterior wave problems to setup the interface condition. In particular, the number of FEM and BEM problems to be solved is twice the number of degrees of freedom required to approximate the unknown interface function.…”

Section: Introductionmentioning

confidence: 99%

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An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: Formulation, analysis, algorithm, and simulation

Domínguez

Ganesh

Sayas

2020

Journal of Computational Physics

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A natural medium for wave propagation comprises a coupled bounded heterogeneous region and an unbounded homogeneous free-space. Frequency-domain wave propagation models in the medium, such as the variable coefficient Helmholtz equation, include a faraway decay radiation condition (RC). It is desirable to develop algorithms that incorporate the full physics of the heterogeneous and unbounded medium wave propagation model, and avoid an approximation of the RC. In this work we first present and analyze an overlapping decomposition framework that is equivalent to the full-space heterogeneous-homogenous continuous model, governed by the Helmholtz equation with a spatially dependent refractive index and the RC. Our novel overlapping framework allows the user to choose two free boundaries, and gain the advantage of applying established high-order finite and boundary element methods (FEM and BEM) to simulate an equivalent coupled model.The coupled model comprises auxiliary interior bounded heterogeneous and exterior unbounded homogeneous Helmholtz problems. A smooth boundary can be chosen for simulating the exterior problem using a spectrally accurate BEM, and a simple boundary can be used to setup a high-order FEM for the interior problem. Thanks to the spectral accuracy of the exterior computational model, the resulting coupled system in the overlapping region is relatively very small. Using the decomposed equivalent framework, we develop a novel overlapping FEM-BEM algorithm for simulating the acoustic or electromagnetic wave propagation in two dimensions. Our FEM-BEM algorithm for the full-space model incorporates the RC exactly. Numerical experiments demonstrate the efficiency of the FEM-BEM approach for simulating smooth and non-smooth wave fields, with the latter induced by a complex heterogeneous medium and a discontinuous refractive index.

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“…However, even with an artificially truncated domain, approximation of the SRC may be avoided by using a hybrid of the FEM and the boundary element method (BEM). This can be achieved by developing an exact interface condition to match the interior and exterior absorbed total fields at the interface between the bounded heterogeneous and unbounded homogeneous media (see and references therein). For high‐order simulations, it is important to make sure that the artificial interface in the model is smooth.…”

Section: Introductionmentioning

confidence: 99%

An efficient multigrid algorithm for heterogeneous acoustic media sign‐indefinite high‐order FEM models

Ganesh

Morgenstern

2016

Numerical Linear Algebra App

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Summary Large‐scale scientific computing models are needed for the simulation of wave propagation especially for multiple frequency and high‐frequency models in complex heterogeneous media. Multigrid methods provide efficient iterative solvers for many large sign‐definite systems of equations resulting from physical models. Time‐harmonic wave propagation models lead to sign‐indefinite systems with eigenvalues in the left half of the complex plane. Thus standard multigrid approaches applied in conjunction with a low‐order finite difference or finite element method are not sufficient. In this work, we describe a high‐order finite element method model for multiple (low to high) frequency time‐harmonic acoustic wave propagation on general curved, non‐convex, and non‐smooth domains with heterogeneous media using a multigrid approximation of the shifted Laplacian operator as a preconditioner. We implement the model using an efficient geometric multigrid approach with parallel grid transfer operator calculations to simulate the model using the BiCGStab iterative solver. We demonstrate the efficiency and parallel performance of the computational model with multiple low (5 wavelength) to high‐frequency (100 wavelength) input incident waves. Copyright © 2016 John Wiley & Sons, Ltd.

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High-order FEM–BEM computer models for wave propagation in unbounded and heterogeneous media: Application to time-harmonic acoustic horn problem

Cited by 23 publications

References 12 publications

High-order finite element–integral equation coupling on embedded meshes

High-order finite element–integral equation coupling on embedded meshes

An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media: Formulation, analysis, algorithm, and simulation

An efficient multigrid algorithm for heterogeneous acoustic media sign‐indefinite high‐order FEM models

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