Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions

Gordon, Dan; Gordon, Rachel; Turkel, Eli

doi:10.1016/j.jcp.2015.05.027

Cited by 20 publications

(24 citation statements)

References 37 publications

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“…Namely, we calculate the average value between the loads on the adjacent nodes to a corner node A . Different solutions to the corner problem are given by Bamberger et al and Gordon et al…”

Section: Trac With Second‐order Absorbing Boundary Condition: Finite mentioning

confidence: 99%

“…Namely, we calculate the average value between the loads on the adjacent nodes to a corner node A. Different solutions to the corner problem are given by Bamberger et al 26 and Gordon et al 27 The time stepping scheme is performed by substituting all rows A ∈ V in the matrix G, where V is the set of the corner nodes, by the average of its adjacent rows A 1 and A 2 , ie, G(A, ∶) ← 1 2 G(A 1 , ∶) + 1 2 G(A 2 , ∶). Then, Algorithm 4 is used for the time stepping.…”

Section: Corner Node Treatmentmentioning

confidence: 99%

“…On Γ q , we impose the second-order ABC (12). Given the boundary conditions on Γ q and Γ u , (12) and (31) respectively, we observe that the solution of the wave problem in Ω is the scattered field of the obstacle D, created by the plane wave g (27). Indeed, since u S = u T − u I , see (2), and u T = 0 on the boundaries of the rigid scatterer, (31) is obtained.…”

Section: Numerical Setupmentioning

confidence: 99%

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Obstacle identification using the TRAC algorithm with a second‐order ABC

Levin

Turkel

Givoli

2019

Numerical Meth Engineering

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Summary We consider obstacle identification using wave propagation. In such problems, one wants to find the location, shape, and size of an unknown obstacle from given measurements. We propose an algorithm for the identification task based on a time‐reversed absorbing condition (TRAC) technique. Here, we apply the TRAC method to time‐dependent linear acoustics, although our methodology can be applied to other wave‐related problems as well, such as elastodynamics. There are two main contributions of our identification algorithm. The first contribution is the development of a robust and effective method for obstacle identification. While the original paper presented criteria for accepting or rejecting regions that enclose the obstacle, we use these criteria to develop an algorithm that automatically identifies the location of the obstacle. The second contribution is the utilization of an improved absorbing boundary condition (ABC) for the identification. We use the second‐order Engquist‐Majda ABC, and we implement it with a finite element scheme. To our knowledge, this is the first time that the second‐order Engquist‐Majda ABC is employed with the finite element method, as this boundary condition does not naturally fit in finite element schemes in its original form. Numerical experiments for the algorithms are presented.

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“…Namely, we calculate the average value between the loads on the adjacent nodes to a corner node A . Different solutions to the corner problem are given by Bamberger et al and Gordon et al…”

Section: Trac With Second‐order Absorbing Boundary Condition: Finite mentioning

confidence: 99%

Section: Corner Node Treatmentmentioning

confidence: 99%

Section: Numerical Setupmentioning

confidence: 99%

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Obstacle identification using the TRAC algorithm with a second‐order ABC

Levin

Turkel

Givoli

2019

Numerical Meth Engineering

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“…This approach is particularly suitable for our finite-element framework since the gradient information is already available at every time step in our simulations. The use of the field gradient information in the absorbing conditions was already investigated for the Helmholtz equation in [13]. There it was proposed to replace the normal derivatives that appear in the absorbing conditions by the derivatives in the direction of the wave propagation.…”

Section: Introductionmentioning

confidence: 99%

“…There it was proposed to replace the normal derivatives that appear in the absorbing conditions by the derivatives in the direction of the wave propagation. In the linear regime, our approach can be understood as an extension of the gradient method in [13] for a time-dependent wave model.…”

Section: Introductionmentioning

confidence: 99%

Self-adaptive absorbing boundary conditions for quasilinear acoustic wave propagation

Muhr

Nikolić

Wohlmuth

2019

Journal of Computational Physics

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We propose a self-adaptive absorbing technique for quasilinear ultrasound waves in twoand three-dimensional computational domains. As a model for the nonlinear ultrasound propagation in thermoviscous fluids, we employ Westervelt's wave equation solved for the acoustic velocity potential. The angle of incidence of the wave is computed based on the information provided by the wave-field gradient which is readily available in the finite element framework. The absorbing boundary conditions are then updated with the angle values in real time. Numerical experiments illustrate the accuracy and efficiency of the proposed method.

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Are you using the right tools in computational electromagnetics?

Sankaran¹

2019

Engineering Reports

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Have you ever wondered why we use certain computational electromagnetics methods and how we decide on the choice of tools for modeling problems in electromagnetics? Though true for any field, particularly in electrodynamics, there is a gap between current practitioners' knowledge and knowhow about different tools and the state‐of‐the‐art developments. Rapid advancements made in material science and (nano)‐fabrication techniques are demanding new tools with multiscale and multiphysics capabilities. In this article, we cover the recent developments and highlight capabilities and limitations of different electromagnetic modeling tools. One has to answer a series of questions about modeling constraints and objectives before picking the appropriate tool. We aim to clarify some of the misconceptions, discuss limits and capabilities of some of the popular electromagnetic modeling tools, and provide a few practical tips, so that applied physicists and engineers can make informed decisions while choosing appropriate tools for their applications.

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Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions

Cited by 20 publications

References 37 publications

Obstacle identification using the TRAC algorithm with a second‐order ABC

Obstacle identification using the TRAC algorithm with a second‐order ABC

Self-adaptive absorbing boundary conditions for quasilinear acoustic wave propagation

Are you using the right tools in computational electromagnetics?

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