论文标题
用于DPG方法的自适应多移民求解器，并在线性声学和电磁学中应用
An adaptive multigrid solver for DPG methods with applications in linear acoustics and electromagnetics
论文作者
论文摘要
我们提出了一种自适应多移民预处理技术，用于求解由不连续的彼得罗夫 - 加勒金（DPG）离散化引起的线性系统。与标准的多机技术不同，该预处理仅涉及在网格骨骼上定义的痕量空间，并且适用于自适应HP-MESHES。构建的关键点是将迭代求解器与DPG技术提供的全自动且可靠的网状精炼过程集成在一起。溶液技术的功效通过了许多线性声学和电磁模拟的示例，包括高频制度中的模拟，否则这些问题将是棘手的。最后，我们分析了均匀网格的一级预处理（更平滑），并证明可以基于良好的自我关节积极确定运算符的理论得出了预处理线性系统条件数的理论估计。
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.
