论文标题
helmholtz方程的等几何解，具有差异边界条件：数值体验
Isogeometric solution of Helmholtz equation with Dirichlet boundary condition: numerical experiences
论文作者
论文摘要
在本文中，我们使用iSODENOTRIC方法在有界物理结构域上使用非均匀的Dirichlet边界条件求解Helmholtz方程。从问题的变化公式开始，我们展示了如何应用同几何方法，以使用生物段B-Spline函数获得溶液的近似值。为了说明该方法的功能，我们解决了几个困难问题，这些问题是Helmholtz方程的特殊情况，其中该解决方案在某些点上具有不连续的梯度，或者它具有高度振荡性。对于这些问题，我们解释了如何选择B-Spline二次函数的结，以及如何插入知道结，以便获得具有不规则边界区域的精确溶液的良好近似值。通过我们的朱莉娅实施该方法获得的结果证明，同几年方法可产生相对小的误差和计算成本的近似值。
In this paper we use the Isogeometric method to solve the Helmholtz equation with nonhomogeneous Dirichlet boundary condition over a bounded physical domain. Starting from the variational formulation of the problem, we show with details how to apply the isogeometric approach to obtain an approximation of the solution using biquadratic B-spline functions. To illustrate the power of the method we solve several difficult problems, which are particular cases of the Helmholtz equation, where the solution has discontinuous gradient in some points, or it is highly oscillatory. For these problems we explain how to select the knots of B-spline quadratic functions and how to insert knew knots in order to obtain good approximations of the exact solution on regions with irregular boundary. The results, obtained with our Julia implementation of the method, prove that isogeometric approach produces approximations with a relative small error and computational cost.
