论文标题
3D对流的Helmholtz方程的三种类型的准特性函数：结构和近似属性
Three types of quasi-Trefftz functions for the 3D convected Helmholtz equation: construction and approximation properties
论文作者
论文摘要
TREFFTZ方法是用于近似边界和/或初始值问题的近似值的数值方法。它们是具有特定测试和试验功能的Galerkin方法，可以在局部解决局部微分方程（PDE）。此属性称为TREFFTZ属性。引入了准Trefftz方法，以利用Trefftz方法的优势来解决由可变系数PDES管辖的问题，通过将Trefftz属性放松到所谓的准Trefftz属性中：测试和试验功能不是严重的解决方案，而是对pde的局部近似解决方案。为了开发由对流的Helmholtz方程控制的空气声学问题的Quassi-Trefftz方法，目前的工作解决了三个Quasi-Trefftz函数的定义，构建和近似特性的问题：两个基于对平面波解决方案的概括，以及一项polynomial的问题。多项式基础显示出巨大的希望，因为它不会遭受像波般的基础固有的不良条件问题。
Trefftz methods are numerical methods for the approximation of solutions to boundary and/or initial value problems. They are Galerkin methods with particular test and trial functions, which solve locally the governing partial differential equation (PDE). This property is called the Trefftz property. Quasi-Trefftz methods were introduced to leverage the advantages of Trefftz methods for problems governed by variable coefficient PDEs, by relaxing the Trefftz property into a so-called quasi-Trefftz property: test and trial functions are not exact solutions but rather local approximate solutions to the governing PDE. In order to develop quassi-Trefftz methods for aero-acoustics problems governed by the convected Helmholtz equation, the present work tackles the question of the definition, construction and approximation properties of three families of quasi-Trefftz functions: two based on generalizations on plane wave solutions, and one polynomial. The polynomial basis shows significant promise as it does not suffer from the ill-conditioning issue inherent to wave-like bases.
