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An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics

机译:具有线性声学和电磁自动应用的DPG方法的自适应多重求解器

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We propose an adaptive multigrid preconditioning technology for solving linear systems arising from Discontinuous Petrov-Galerkin (DPG) discretizations. Unlike standard multigrid techniques, this preconditioner involves only trace spaces defined on the mesh skeleton, and it is suitable for adaptive hp-meshes. The key point of the construction is the integration of the iterative solver with a fully automatic and reliable mesh refinement process provided by the DPG technology. The efficacy of the solution technique is showcased with numerous examples of linear acoustics and electromagnetic simulations, including simulations in the high-frequency regime, problems which otherwise would be intractable. Finally, we analyze the one-level preconditioner (smoother) for uniform meshes and we demonstrate that theoretical estimates of the condition number of the preconditioned linear system can be derived based on well established theory for self-adjoint positive definite operators.
机译:我们提出了一种自适应多国推献预处理技术,用于求解不连续Petrov-Galerkin(DPG)离散化而产生的线性系统。与标准多字端技术不同,该预处理器仅涉及在网状骨架上定义的跟踪空间,并且适用于自适应HP网格。施工的关键点是迭代求解器与DPG技术提供的全自动和可靠的网格细化过程集成。求解溶液技术的效果,具有许多线性声学和电磁模拟的例子,包括在高频状态下模拟,否则是难以相容的问题。最后,我们分析了均匀网格的单级预处理器(更顺畅),我们证明了预先说明的线性系统的条件数量的理论估计可以基于为自伴自伴随的正定定向运算符的良好建立的理论来导出。

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