3D DC Using EXCMG on Unstructured Grids

What is it about?

This study proposes an extrapolation cascadic multigrid method (EXCMG) on unstructured-block tetrahedral grids to solve the large linear system derived from finite element discretization of 3D DC resistivity modeling with topography. It uses a truncated half-sphere computational domain to simplify the Robin boundary condition for the regular secondary potential in 3D media. Starting with a relatively coarse unstructured-block tetrahedral mesh to capture the model’s basic features, it then generates a series of nested meshes via regular refinement.

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Why is it important?

The core innovations of the EXCMG method proposed in this study can be summarized into three points, all designed around "improving the efficiency and accuracy of 3D DC resistivity forward modeling with topography": 1. Optimization of computational domain and boundary conditions: A truncated half-sphere computational domain is adopted to simplify the Robin boundary condition for the "regular secondary potential" in 3D media, avoiding the complexity and error-proneness of traditional boundary processing. 2. Nested mesh generation strategy: Starting with a relatively coarse mesh that can capture the basic features of the model, a series of nested tetrahedral meshes are generated through "regular refinement". This balances the needs of computational efficiency and detailed model characterization. 3. Novel multigrid prolongation operator: The operator is innovatively designed by integrating "Richardson extrapolation" with "second-order tetrahedral interpolation". It can provide a high-quality initial guess for the smoothing operator of the next-level mesh, directly breaking through the bottleneck of slow convergence in traditional operators and significantly improving computational efficiency.