Klein–Gordon equation with advection on unbounded domains using spectral elements and high-order non-reflecting boundary conditions

Lindquist, Joseph M.; Giraldo, Francis X.; Neta, Beny

doi:10.1016/j.amc.2010.07.079

Cited by 9 publications

(6 citation statements)

References 31 publications

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“…The convergence rate coincides with the formal estimate (13) when k = 0. It is worth to notice that in order to satisfy periodicity, the parameters chosen must relate to the width L of the domain respecting L = will not be satisfied) or too small (this would demand a very large domain, since L is inversely proportional to ω).…”

Section: Numerical Resultssupporting

confidence: 55%

“…The imposition of artificial contours and appropriate boundary conditions (BCs) is an aspect to be considered. Among many possibilities, one could use a non-reflecting BC, defined through pseudo-differential operators [1,2,3,4], or choose from a variety of approximate BCs, such as PMLs [5,6,7] or Absorbing Boundary Conditions (ABCs) [8,9,10,11,12,13]. In this work the Hagstrom-Warburton ABC [10,14] is chosen.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Equivalent Boundary Conditions for Heterogeneous Acoustic Media

Castro

Diaz

Péron

2014

Tend. Mat. Apl. Comput.

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ABSTRACT. In this work, we derive high order Equivalent Absorbing Boundary Conditions EABCs that model the propagation of waves in semi-infinite bilayered acoustic media. Our motivation is to restrict the computational domain in the simulation of seismic waves that are propagated from the earth and transmitted to the stratified heterogeneous media composed by ocean and atmosphere. These EABCs are adapted to Hagstrom-Warburton ABCs and appear as first and second order of approximation with respect to a small parameter involved in a multiscale expansion. Computational tests illustrate the accuracy of the first approximate model with respect to the small parameter.

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Section: Numerical Resultssupporting

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Equivalent Boundary Conditions for Heterogeneous Acoustic Media

Castro

Diaz

Péron

2014

Tend. Mat. Apl. Comput.

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“…However, these are not by any means the best way of imposing such NRBCs but is used extensively in many operational weather models (for an example of proper NRBCs, see, e.g., [6,24,23]). To impose a sponge layer boundary condition, one can write the semidiscrete (in time) equations as follows:…”

Section: Boundary Conditionsmentioning

confidence: 99%

Implicit-Explicit Formulations of a Three-Dimensional Nonhydrostatic Unified Model of the Atmosphere (NUMA)

Giraldo¹,

Kelly²,

Constantinescu³

2013

SIAM J. Sci. Comput.

174

234

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We derive an implicit-explicit (IMEX) formalism for the three-dimensional (3D) Euler equations that allow a unified representation of various nonhydrostatic flow regimes, including cloud resolving and mesoscale (flow in a 3D Cartesian domain) as well as global regimes (flow in spherical geometries). This general IMEX formalism admits numerous types of methods including single-stage multistep methods (e.g., Adams methods and backward difference formulas) and multistage singlestep methods (e.g., additive Runge-Kutta methods). The significance of this result is that it allows a numerical model to reuse the same machinery for all classes of time-integration methods described in this work. We also derive two classes of IMEX methods, one-dimensional and 3D, and show that they achieve their expected theoretical rates of convergence regardless of the geometry (e.g., 3D box or sphere) and introduce a new second-order IMEX Runge-Kutta method that performs better than the other second-order methods considered. We then compare all the IMEX methods in terms of accuracy and efficiency for two types of geophysical fluid dynamics problems: buoyant convection and inertia-gravity waves. These results show that the high-order time-integration methods yield better efficiency particularly when high levels of accuracy are desired. Introduction.In a previous article [20] we introduced the nonhydrostatic unified model of the atmosphere (NUMA) for use in limited-area modeling (i.e., mesoscale or regional flow), namely, applications in which the flows are in large, three-dimensional (3D) Cartesian domains (imagine flow in a 3D box where the grid resolutions are below 10 km); the emphasis of that paper was on the performance of the model on distributed-memory computers with a large number of processors. In that paper we showed that the explicit RK35 time integrator (also used in this paper) was able to achieve strong linear scaling for processor counts on the order of 10 5 . The emphasis of the present article is on the mathematical framework of the model dynamics (i.e., we are not considering the subgrid-scale parameterization at this point;

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“…It should be noted that the only other spectral element, high-order boundary approach are Kucherov and Givoli [19] and Lindquist et al [20,13]. Kucherov and Givoli demonstrate exponential error convergence of the classical wave equation on a semi-infinite channel when solved using spectral elements and high order boundary treatment (using the H-W boundary scheme).…”

Section: Introductionmentioning

confidence: 99%

“…This formulation has been previously demonstrated in a finite difference formulation to arbitrarily high NRBC order [12], however, accuracy gains realized by increasing the NRBC ceased after order 2. The formulation used by Lindquist et al [13] remedied this limitation by using a high-order treatment of space (SE) and time (Runge-Kutta) to show the benefits of using the high-order boundary (G-N) scheme. Spectral elements methods used recently by Mitra and Gopalakrishnan [14] and Vinod et al [15] to solve wave propagation problem and by Dorao and 0096-3003/$ -see front matter Published by Elsevier Inc. doi:10.1016/j.amc.2011.…”

Section: Introductionmentioning

confidence: 99%