math.NA · 2026-06-21 · No. 30

Numerical Analysis, 2026-06-21.

3 new papers in math.NA. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

3 entries
  1. 01

    CoarseSolvers for Exascale Solution of Poisson Problems

    Thilina Ratnayaka, Paul Fischer, Luke Olson

    math.NA · cs.DC · cs.MS

    WepresentatwolevelSchwarzmethodasanalternativetoAlgebraicMultigridmethod(AMG) used as the last level (coarse) solver of the p-multigrid pMG preconditioner for pressure Poission equation resulting from Spectral/Finite element descretization of incompressible Navier-Stokes eqaution. Proposed Schwarz method consits of a local problem in the original pMG coarse space and a global coarse problem. Main contribution of the paper is a novel,...

    arxiv.org/abs/2606.20496 · PDF

  2. 02

    Structure-Oriented Randomized Neural Networks for Poisson-Nernst-Planck and Poisson-Nernst-Planck-Navier-Stokes Systems

    Yunlong Li, Fei Wang

    math.NA · cs.LG · physics.comp-ph

    We develop a structure-oriented randomized neural network framework, termed SO-RaNN, for the Poisson-Nernst-Planck (PNP) system and the Poisson-Nernst-Planck-Navier-Stokes (PNP-NS) system. The decoupled linearized subproblems are solved iteratively by randomized neural networks in a space-time framework. For the concentration variables, a pointwise cut-off is used to enforce positivity at the value level, and discrete mass-scaling factors are...

    arxiv.org/abs/2606.19912 · PDF

  3. 03

    A fast direct solver based neural network for solving PDEs

    Jashwanth Reddy Kadaru, Vaishnavi Gujjula

    math.NA · cs.LG

    The matrices arising from large scale $N$-body problems can be efficiently represented using hierarchical matrices, whose key idea is that the admissible off-diagonal sub-matrices can be well approximated by low-rank matrices across a hierarchy of matrix partitions. HODLR (Hierarchical Off-Diagonal Low-Rank) matrices are a subclass of hierarchical matrices in which all off-diagonal submatrices at every level of a recursive binary partition...

    arxiv.org/abs/2606.19895 · PDF

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