论文标题
标量波方程
Hermite-Discontinuous Galerkin Overset Grid Methods for the Scalar Wave Equation
论文作者
论文摘要
我们为波动方程提供了高阶准确的数值方法，该方法将有效的HERMITE方法与使用填充网格相结合的有效的HERMITE方法与具有柔性的不连续的Galerkin方法。接近边界，我们使用薄边界拟合的曲线网格，在体积中，我们使用笛卡尔网格，以便求解器的计算复杂性接近结构化的笛卡尔式Hermite方法。与许多其他收割方法不同，我们不需要添加人造耗散，但是我们发现，赫米特人和不连续的galerkin方法的内置耗散足以保持稳定性。通过数值实验，我们证明了方法在转发和反向问题的稳定性，准确性，效率和适用性。
We present high order accurate numerical methods for the wave equation that combines efficient Hermite methods with eometrically flexible discontinuous Galerkin methods by using overset grids. Near boundaries we use thin boundary fitted curvilinear grids and in the volume we use Cartesian grids so that the computational complexity of the solvers approach a structured Cartesian Hermite method. Unlike many other overset methods we do not need to add artificial dissipation but we find that the built in dissipation of the Hermite and discontinuous Galerkin methods is sufficient to maintain stability. By numerical experiments we demonstrate the stability, accuracy, efficiency and applicability of the methods to forward and inverse problems.
