Non-conforming hybrid meshes for efficient 2-D wave propagation using the Discontinuous Galerkin Method
Non-conforming hybrid meshes for efficient 2-D wave propagation using the Discontinuous Galerkin Method
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DOI：
10.1111/j.1365-246x.2010.04858.x
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发表时间：
2011-02
影响因子：
2.8
通讯作者：
V. Hermann;M. Käser;C. Castro
中科院分区：
文献类型：
--
作者：
V. Hermann;M. Käser;C. Castro
本文提出了一种采用高阶时间积分技术的不连续伽辽金有限元方法，用于二维非协调混合网格的地震波传播建模。该格式可以在空间和时间上实现相同的近似顺序，并避免由于网格转换不一致或单元类型的变化而导致的数值伪影。采用沿相邻元素部分重叠边缘的逐点高斯积分，保证了方案的精度，同时在问题适应网格生成过程中提供了更高的灵活性。我们描述了并行实现的区域分解策略，并通过数值收敛测试和与独立参考解的对比实验验证了新方案的性能。非一致性混合网格的优点是可以选择与地震速度结构成正比的网格间距，这使得即使对于规则的四边形网格也可以进行简单的细化或粗化方法。对于强材料对比和几何薄结构的特殊问题，该方案在内存和运行时间要求方面降低了计算成本。所提出的结果有望实现类似的行为扩展到三维空间，其中四面体和六面体元素的耦合需要不一致的网格过渡，以避免以金字塔的形式连接元素。
SUMMARY We present a Discontinuous Galerkin finite element method using a high-order time integration technique for seismic wave propagation modelling on non-conforming hybrid meshes in two space dimensions. The scheme can be formulated to achieve the same approximation order in space and time and avoids numerical artefacts due to non-conforming mesh transitions or the change of the element type. A point-wise Gaussian integration along partially overlapping edges of adjacent elements is used to preserve the schemes accuracy while providing a higher flexibility in the problem-adapted mesh generation process. We describe the domain decomposition strategy of the parallel implementation and validate the performance of the new scheme by numerical convergence test and experiments with comparisons to independent reference solutions. The advantage of non-conforming hybrid meshes is the possibility to choose the mesh spacing proportional to the seismic velocity structure, which allows for simple refinement or coarsening methods even for regular quadrilateral meshes. For particular problems of strong material contrasts and geometrically thin structures, the scheme reduces the computational cost in the sense of memory and run-time requirements. The presented results promise to achieve a similar behaviour for an extension to three space dimensions where the coupling of tetrahedral and hexahedral elements necessitates non-conforming mesh transitions to avoid linking elements in form of pyramids.