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首页> 外文期刊>Journal of Computational Physics >High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics
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High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics

机译：声学与弹性动力学的高阶隐式可混合不连续伽勒金方法

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摘要

We present a class of hybridizable discontinuous Galerkin (HDG) methods for the numerical simulation of wave phenomena in acoustics and elastodynamics. The methods are fully implicit and high-order accurate in both space and time, yet computationally attractive owing to their following distinctive features. First, they reduce the globally coupled unknowns to the approximate trace of the velocity, which is defined on the element faces and single-valued, thereby leading to a significant saving in the computational cost. In addition, all the approximate variables (including the approximate velocity and gradient) converge with the optimal order of k+1 in the L2-norm, when polynomials of degree k≥0 are used to represent the numerical solution and when the time-stepping method is accurate with order k+1. When the time-stepping method is of order k+2, superconvergence properties allows us, by means of local postprocessing, to obtain better, yet inexpensive approximations of the displacement and velocity at any time levels for which an enhanced accuracy is required. In particular, the new approximations converge with order k+2 in the L2-norm when k≥1 for both acoustics and elastodynamics. Extensive numerical results are provided to illustrate these distinctive features.
机译：我们提出了一类可混合的不连续Galerkin（HDG）方法，用于对声学和弹性动力学中的波现象进行数值模拟。这些方法在空间和时间上都是完全隐式的和高阶的，但由于它们具有以下独特性，因此在计算上具有吸引力。首先，它们将全局耦合的未知数减少为近似的速度轨迹，该速度轨迹定义在元素面上并且是单值的，从而显着节省了计算成本。此外，当使用阶数k≥0的多项式表示数值解时，以及当时间步长为L2范数时，所有近似变量（包括近似速度和梯度）都以L + 1范数的k + 1最优顺序收敛。方法对于k + 1阶是准确的。当时间步长方法为k + 2阶时，超收敛特性使我们能够通过局部后处理在需要提高精度的任何时间水平上获得更好，更便宜的位移和速度近似值。特别是，对于声学和弹性动力学，当k≥1时，新的近似值在L2-范数中收敛于k + 2阶。提供了大量的数值结果来说明这些独特的功能。

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