McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation
Solving heterogeneous Helmholtz equations at high wavenumbers remains challenging because the discretized operator is indefinite, pollution degrades phase accuracy, and scalar coarse-grid correction can discard the local phase and propagation-direction information carried by oscillatory errors. We propose Multi-channel Multigrid (McMg), a learned phase-space multigrid preconditioner for heterogeneous Helmholtz equations. Rather than predicting the solution directly, McMg maps residuals to corrections within an iterative framework. Its central idea is to coarsen physical space while retaining unresolved local wave information in the channel dimension: each coarse node carries a learned pac...
| Authors | Jiwei Jia, Xinliang Liu, Juntao Wang et al. |
|---|---|
| Primary category | math.NA |
| Published | 29 June 2026 |
| Last updated at source | 2 July 2026 |
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