2018/10/01 by Anthony Goddard, Andrew J. Wathen, Goddard, Anthony +1 · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Antenna Design and Optimization #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1810.00615
openalex publication_date 2018/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
McDonald, Pestana and Wathen (SIAM J. Sci. Comput. 40(2), pp. A2012-A1033, 2018) present a method for preconditioning of time-dependent PDEs via approximation by a nearby time-periodic problem, that is, they employ circulant-related matrices as preconditioners for the non-symmetric block Toeplitz matrices which arise from an all-at-once formulation. They suggest that such an approach might be efficiently implemented in parallel. In this short article, we present parallel numerical results for their preconditioner which exhibit strong scaling. We also extend their preconditioner via a Neumann series approach, which also allows for efficient parallel execution. Our simple implementation (in C++ and MPI) is available at the Git repository PARALAAOMPI. https://github.com/anthonyjamesgoddard/PARALAAOMPI