Wavenumber-Explicit hp-BEM for High Frequency Scattering
Wavenumber-Explicit hp-BEM for High Frequency Scattering
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用于高频散射的波数显式 hp-BEM
DOI：
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发表时间：
2011
影响因子：
2.9
通讯作者：
J. Melenk
中科院分区：
文献类型：
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作者：
M. Löhndorf;J. Melenk
对于Helmholtz方程(波数为k)和解析曲线或曲面，我们分析了经典组合场积分方程在$L^2环境下的Galerkin离散化。我们给出了保证Galerkin方法稳定性和准最优性的抽象条件。特别注意$hp$-版本的边界元方法($hp$-BEM)。在解算子多项式增长的假设下，证明了当满足以下尺度分解条件时，$hp$-BEM的稳定性和拟最优性：多项式次数$p$至少为$O(\logk)$，且$kh/p$由一个足够小但独立于$k$的数所有界.在这一假设下，准最优估计中的常数与$k$无关。二维数值例子说明了理论结果，甚至表明，在许多情况下，在较弱的条件下，$kh/p$足够小时，给出了准最优性。
For the Helmholtz equation (with wavenumber $k$) and analytic curves or surfaces $\Gamma$, we analyze the Galerkin discretization of classical combined field integral equations in an $L^2$-setting. We give abstract conditions on the approximation properties of the ansatz space that ensure stability and quasi-optimality of the Galerkin method. Special attention is paid to the $hp$-version of the boundary element method ($hp$-BEM). Under the assumption of polynomial growth of the solution operator we show stability and quasi-optimality of the $hp$-BEM if the following scale resolution condition is satisfied: the polynomial degree $p$ is at least $O(\log k)$ and $kh/p$ is bounded by a number that is sufficiently small, but independent of $k$. Under this assumption, the constant in the quasi-optimality estimate is independent of $k$. Numerical examples in two dimensions illustrate the theoretical results and even suggest that in many cases quasi-optimality is given under the weaker condition that $kh/p$ is sufficiently small.
声散射中组合势边界积分算子的条件数估计
影响因子：
0.8
作者：
Chandler-Wilde S
通讯作者：
Chandler-Wilde S