论文标题
非线性kerr型媒体中的多尺度散射
Multiscale Scattering in Nonlinear Kerr-Type Media
论文作者
论文摘要
我们提出了一种多尺度的方法，用于非线性Helmholtz问题，具有KERR系数，折射率和扩散系数的振荡。该方法不依赖于系数上的结构假设，并将称为局部正交分解的多尺度技术与非线性的自适应迭代近似。我们严格地根据适当的假设和离散参数的合适假设来严格地分析适当性和收敛属性的方法。数值示例说明了理论误差估计并强调该方法的实用性。
We propose a multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient. The method does not rely on structural assumptions on the coefficients and combines the multiscale technique known as Localized Orthogonal Decomposition with an adaptive iterative approximation of the nonlinearity. We rigorously analyze the method in terms of well-posedness and convergence properties based on suitable assumptions on the initial data and the discretization parameters. Numerical examples illustrate the theoretical error estimates and underline the practicability of the approach.
