A reflectionless discrete perfectly matched layer

Chern, Albert

doi:10.1016/j.jcp.2018.12.026

Cited by 28 publications

(10 citation statements)

References 74 publications

(119 reference statements)

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“…Differently from Eq. ( 7), an exponential growth of the damping ratio with the distance to the boundary was derived by Chern (2019). In each incremental step of the MPM calculation, the particle velocities are firstly mapped to the surrounding nodes (refer to Dong (2020) for detailed description of the MPM algorithm); then, the dashpot or damping layer ABC can be implemented by adjusting the nodal velocities using Eqs.…”

Section: Methodsmentioning

confidence: 99%

Implementation of absorbing boundary conditions in dynamic simulation of the material point method

Shan

Liao

Dong

et al. 2021

J. Zhejiang Univ. Sci. A

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Outgoing waves arising from high-velocity impacts between soil and structure can be reflected by the conventional truncated boundaries. Absorbing boundary conditions (ABCs), to attenuate the energy of the outward waves, are necessary to ensure the proper representation of the kinematic field and the accurate quantification of impact forces. In this paper, damping layer and dashpot ABCs are implemented in the material point method (MPM) with slight adjustments. Benchmark scenarios of different dynamic problems are modelled with the ABCs configured. Feasibility of the ABCs is assessed through the velocity fluctuations at specific observation points and the impact force fluctuations on the structures. The impact forces predicted by the MPM with ABCs are verified by comparison with those estimated using a computational fluid dynamics approach.

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Section: Methodsmentioning

confidence: 99%

Implementation of absorbing boundary conditions in dynamic simulation of the material point method

Shan

Liao

Dong

et al. 2021

J. Zhejiang Univ. Sci. A

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“…The open parts of the models were surrounded with a 10-voxel perfectly matched layer, as described by Chern [28], providing anechoic boundaries. The simulated stepwell surfaces were hard, with no sound absorption introduced.…”

Section: Modelling and Simulationmentioning

confidence: 99%

Sound Reflections in Indian Stepwells: Modelling Acoustically Retroreflective Architecture

Cabrera

Holmes

et al. 2022

Acoustics

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Retroreflection is rarely used as a surface treatment in architectural acoustics but is found incidentally with building surfaces that have many simultaneously visible concave right-angle trihedral corners. Such surfaces concentrate reflected sound onto the sound source, mostly at high frequencies. This study investigated the potential for some Indian stepwells (stepped ponds, known as a kund or baori/baoli in Hindi) to provide exceptionally acoustically retroreflective semi-enclosed environments because of the unusually large number of corners formed by the steps. Two cases—Panna Meena ka Kund and Lahan Vav—were investigated using finite-difference time-domain (FDTD) acoustic simulation. The results are consistent with retroreflection, showing reflected energy concentrating on the source position mostly in the high-frequency bands (4 kHz and 2 kHz octave bands). However, the larger stepped pond has substantially less retroreflection, even though it has many more corners, because of the greater diffraction loss over the longer distances. Retroreflection is still evident (but reduced) with non-right-angle trihedral corners (80–100°). The overall results are sufficiently strong to indicate that acoustic retroreflection should be audible to an attuned visitor in benign environmental conditions, at least at moderately sized stepped ponds that are in good geometric condition.

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“…Oscillatory systems such as the Helmholtz equation and wave equations are more sensitive to the choice of the boundary condition. Absorbing boundary conditions (ABCs) [Engquist and Majda 1977] and perfectly matched layers (PMLs) [Berenger 1994;Chern 2019] are the suitable boundary conditions that reduce the reflection waves. These non-reflecting boundary conditions have been applied to fluid surface simulations [Söderström et al 2010;Bojsen-Hansen and Wojtan 2016] and wave-based acoustic synthesis [James 2016;Wang et al 2018] in an open space.…”

Section: Related Workmentioning

confidence: 99%

Kelvin transformations for simulations on infinite domains

2021

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Solving partial differential equations (PDEs) on infinite domains has been a challenging task in physical simulations and geometry processing. We introduce a general technique to transform a PDE problem on an unbounded domain to a PDE problem on a bounded domain. Our method uses the Kelvin Transform, which essentially inverts the distance from the origin. However, naive application of this coordinate mapping can still result in a singularity at the origin in the transformed domain. We show that by factoring the desired solution into the product of an analytically known (asymptotic) component and another function to solve for, the problem can be made continuous and compact, with solutions significantly more efficient and well-conditioned than traditional finite element and Monte Carlo numerical PDE methods on stretched coordinates. Specifically, we show that every Poisson or Laplace equation on an infinite domain is transformed to another Poisson (Laplace) equation on a compact region. In other words, any existing Poisson solver on a bounded domain is readily an infinite domain Poisson solver after being wrapped by our transformation. We demonstrate the integration of our method with finite difference and Monte Carlo PDE solvers, with applications in the fluid pressure solve and simulating electromagnetism, including visualizations of the solar magnetic field. Our transformation technique also applies to the Helmholtz equation whose solutions oscillate out to infinity. After the transformation, the Helmholtz equation becomes a tractable equation on a bounded domain without infinite oscillation. To our knowledge, this is the first time that the Helmholtz equation on an infinite domain is solved on a bounded grid without requiring an artificial absorbing boundary condition.

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A reflectionless discrete perfectly matched layer

Cited by 28 publications

References 74 publications

Implementation of absorbing boundary conditions in dynamic simulation of the material point method

Implementation of absorbing boundary conditions in dynamic simulation of the material point method

Sound Reflections in Indian Stepwells: Modelling Acoustically Retroreflective Architecture

Kelvin transformations for simulations on infinite domains

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