论文标题
非本地Helmholtz方程的完美匹配层II：多维情况
Perfectly Matched Layers for nonlocal Helmholtz equations II: multi-dimensional cases
论文作者
论文摘要
完美匹配的层（PML）是配制的，并应用于一个和二维的数值求解非局部helmholtz方程。在一个维度中，我们介绍了具有一般内核的非本地Helmholtz方程的PML修改，理论上在某种意义上显示了其有效性。在两个维度中，我们在两个笛卡尔坐标和极性坐标中进行PML修饰。基于PML修饰，非本地Helmholtz方程在一个和二维空间中被截断，并引入了渐近兼容性方案，以使所得的截断问题离散。最后，提供了数值示例来研究PML的“数值反射”，并证明了我们非本地PML策略的有效性和验证。
Perfectly matched layers (PMLs) are formulated and applied to numerically solve nonlocal Helmholtz equations in one and two dimensions. In one dimension, we present the PML modifications for the nonlocal Helmholtz equation with general kernels and theoretically show its effectiveness in some sense. In two dimensions, we give the PML modifications in both Cartesian coordinates and polar coordinates. Based on the PML modifications, nonlocal Helmholtz equations are truncated in one and two dimensional spaces, and asymptotic compatibility schemes are introduced to discretize the resulting truncated problems. Finally, numerical examples are provided to study the "numerical reflections" by PMLs and demonstrate the effectiveness and validation of our nonlocal PML strategy.
