When is the error in the $$h$$ h -BEM for solving the Helmholtz equation bounded independently of $$k$$ k ?
When is the error in the $$h$$ h -BEM for solving the Helmholtz equation bounded independently of $$k$$ k ?
复制标题
求解亥姆霍兹方程的 $$h$$ h -BEM 中的误差何时独立于 $$k$$ k 有界？
DOI：
10.1007/s10543-014-0501-5
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发表时间：
2014
影响因子：
1.5
通讯作者：
Graham I
中科院分区：
文献类型：
--
作者：
Graham I
我们考虑用标准的第二类组合场积分方程解Helmholtz方程的声-软散射问题。我们得到了相对最佳逼近误差独立于有界的充分条件。对于某些几何形状，这些严格地证明了普遍持有的信念的合理性，即每个波长的固定自由度足以保持相对最佳逼近误差的有界，而不依赖于。然后，我们得到了Galerkin方法是准最优的充分条件，并且准最优性的常数独立于。数值实验表明，虽然这些准最优性条件是充分的，但对于许多几何形状来说，它们并不是必需的。
We consider solving the sound-soft scattering problem for the Helmholtz equation with the-version of the boundary element method using the standard second-kind combined-field integral equations. We obtain sufficient conditions for the relative best approximation error to be bounded independently of. For certain geometries, these rigorously justify the commonly-held belief that a fixed number of degrees of freedom per wavelength is sufficient to keep the relative best approximation error bounded independently of. We then obtain sufficient conditions for the Galerkin method to be quasi-optimal, with the constant of quasi-optimality independent of. Numerical experiments indicate that, while these conditions for quasi-optimality are sufficient, they are not necessary for many geometries.