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首页> 外文期刊>Journal of Computational Physics >Phase reduction models for improving the accuracy of the finite element solution of time-harmonic scattering problems I: General approach and low-order models
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Phase reduction models for improving the accuracy of the finite element solution of time-harmonic scattering problems I: General approach and low-order models

机译：用于提高时谐散射问题有限元解的精度的相减模型I：通用方法和低阶模型

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This paper introduces a new formulation of high frequency time-harmonic scattering problems in view of a numerical finite element solution. it is well-known that pollution error causes inaccuracies in the finite element solution of short-wave problems. To partially avoid this precision problem, the strategy proposed here consists in firstly numerically computing at a low cost an approximate phase of the exact solution through asymptotic propagative models. Secondly, using this approximate phase, a slowly varying unknown envelope is introduced and is computed using coarser mesh grids. The global procedure is called Phase Reduction. In this first paper, the general theoretical procedure is developed and low-order propagative models are numerically investigated in detail. Improved solutions based on higher order models are discussed showing the potential of the method for further developments. (C) 2009 Elsevier Inc. All rights reserved.
机译：鉴于数值有限元解，本文介绍了一种高频时谐散射问题的新公式。众所周知，污染误差会导致短波问题的有限元求解不准确。为了部分避免这种精度问题，这里提出的策略包括首先通过渐近传播模型以低成本对精确解的近似相位进行数值计算。其次，使用这个近似相位，引入一个缓慢变化的未知包络，并使用较粗的网格进行计算。全局过程称为相减少。在第一篇论文中，发展了一般的理论程序，并对低阶传播模型进行了详细的数值研究。讨论了基于高阶模型的改进解决方案，显示了该方法进一步发展的潜力。 （C）2009 Elsevier Inc.保留所有权利。

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