Pith Number

pith:N6RR6BTJ

pith:2026:N6RR6BTJLHDHGHAJHEQVMS5WQ2

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Implicit Dynamical Tensor Train Approximation for Kinetic Equations with Stiff Fokker--Planck Collisions

Geshuo Wang, Jingwei Hu

An implicit dynamical low-rank method in tensor-train format overcomes stability constraints for kinetic equations with stiff Fokker-Planck collisions.

arxiv:2605.15382 v1 · 2026-05-14 · math.NA · cs.NA · math.AP

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Claims

C1strongest claim

The proposed implicit or IMEX dynamical low-rank method in tensor-train format overcomes the severe stability constraints of explicit schemes in strongly collisional regimes while preserving linear scaling with respect to the number of grid points in a single velocity dimension.

C2weakest assumption

That the Sylvester equations arising in the implicit substeps admit stable, structure-preserving direct solutions whose accuracy and low-rank property are not degraded by the implicit treatment or by the specific form of the nonlinear Fokker-Planck operator.

C3one line summary

An implicit dynamical tensor-train method for stiff kinetic equations with Fokker-Planck collisions that formulates substeps as Sylvester equations solved by direct structured solvers.

References

44 extracted · 44 resolved · 0 Pith anchors

[1] Appel¨ o and Y 2025

[2] U. Banik and A. Bhattacharjee. Relaxation of weakly collisional plasma: Continuous spectra, discrete eigenmodes, and the decay of echoes.Phys. Rev. E, 110(4):045204, 2024 2024

[3] R. Bartels and G. Stewart. Algorithm 432: Solution of the matrix equationAX+XB=C.Comm. ACM, 15:820–826, 1972 1972

[4] C. Black, K. Germaschewski, A. Bhattacharjee, and C. Ng. Discrete kinetic eigenmode spectra of electron plasma oscillations in weakly collisional plasma: A numerical study.Phys. Plasmas, 20(1), 2013 2013

[5] Cercignani.The Boltzmann Equation and Its Applications 1988

Formal links

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Receipt and verification

First computed	2026-05-20T00:00:55.574929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fa31f066959c6731c093921564bb686b8e6ef931920980021c9519e3b987c64

Aliases

arxiv: 2605.15382 · arxiv_version: 2605.15382v1 · doi: 10.48550/arxiv.2605.15382 · pith_short_12: N6RR6BTJLHDH · pith_short_16: N6RR6BTJLHDHGHAJ · pith_short_8: N6RR6BTJ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/N6RR6BTJLHDHGHAJHEQVMS5WQ2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 6fa31f066959c6731c093921564bb686b8e6ef931920980021c9519e3b987c64

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "72cd74cb7f523fbfe9afeaa6d89f95a19f619cb18c6d1b0c2f3f9b8e58b0cc59",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-14T20:12:21Z",
    "title_canon_sha256": "574a352bcbbab760041106f5dc682d38bed0e17d9c547f6bfe798db744ccd3bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15382",
    "kind": "arxiv",
    "version": 1
  }
}