标题： 无矩阵并行可扩展多级缺陷化预条件方法用于异构时谐波问题 显示英文标题

标题： Matrix-Free Parallel Scalable Multilevel Deflation Preconditioning for Heterogeneous Time-Harmonic Wave Problems

摘要： 我们提出了一种无矩阵的并行可扩展多级归一化预处理方法，用于异构时谐波问题。 在Dwarka和Vuik（SIAM J. Sci. Comput. 42(2):A901-A928, 2020; J. Comput. Phys. 469:111327, 2022）针对高度不定时谐波提出的高阶归一化预处理方法的基础上，我们将这些技术适应于并行实现，以在解决大规模异构问题时最小化污染误差。 我们提出的方法将复数位移拉普拉斯预处理器与归一化方法相结合。 我们采用从伽辽金粗化方法中得出的高阶归一化向量和重新离散化方案，用于无矩阵的并行实现。 我们建议了一种稳健且高效的无矩阵多级归一化方法配置，该配置可实现接近波数无关的收敛性和良好的时间效率。 数值实验表明了我们的方法在日益复杂的模型问题中的有效性。 预处理Krylov子空间方法的无矩阵实现减少了内存消耗，并且并行框架表现出令人满意的并行性能和弱并行可扩展性。 这项工作标志着在为波动传播中的大规模实际应用开发高效、可扩展和并行的多级归一化预处理方法方面迈出了重要一步。 显示英文摘要

摘要： We present a matrix-free parallel scalable multilevel deflation preconditioned method for heterogeneous time-harmonic wave problems. Building on the higher-order deflation preconditioning proposed by Dwarka and Vuik (SIAM J. Sci. Comput. 42(2):A901-A928, 2020; J. Comput. Phys. 469:111327, 2022) for highly indefinite time-harmonic waves, we adapt these techniques for parallel implementation in the context of solving large-scale heterogeneous problems with minimal pollution error. Our proposed method integrates the Complex Shifted Laplacian preconditioner with deflation approaches. We employ higher-order deflation vectors and re-discretization schemes derived from the Galerkin coarsening approach for a matrix-free parallel implementation. We suggest a robust and efficient configuration of the matrix-free multilevel deflation method, which yields a close to wavenumber-independent convergence and good time efficiency. Numerical experiments demonstrate the effectiveness of our approach for increasingly complex model problems. The matrix-free implementation of the preconditioned Krylov subspace methods reduces memory consumption, and the parallel framework exhibits satisfactory parallel performance and weak parallel scalability. This work represents a significant step towards developing efficient, scalable, and parallel multilevel deflation preconditioning methods for large-scale real-world applications in wave propagation.