Pith Number

pith:IEYVL62R

pith:2026:IEYVL62RE7KYAI4RYUGVTC5RL5

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A Tearing and Interconnecting Formulation for Magneto-Quasi-Statics

Clemens Pechstein

A space splitting into gradient fields and a complementary part makes subdomain operators invertible in a tearing-and-interconnecting formulation for the eddy current model.

arxiv:2605.15636 v1 · 2026-05-15 · math.NA · cs.NA

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Claims

C1strongest claim

Under a mild condition on that splitting, it is shown that (i) one does not need any gradient part in the non-conducting domain, and therefore no coupling of any gradient components between the two subdomains, (ii) both subdomain operators are invertible, and (iii) although the magnetic vector potential is discontinuous across the subdomain interface, the corresponding magnetic field is globally in H(div).

C2weakest assumption

The mild condition on the splitting of the space into gradient fields and a complementary space (invoked in the abstract to establish properties (i)-(iii) and overcome interface kernel issues).

C3one line summary

A domain decomposition formulation for magneto-quasi-statics that removes gradient components from the insulating subdomain via space splitting, ensuring invertible operators and global H(div) regularity under a mild condition.

References

32 extracted · 32 resolved · 0 Pith anchors

[1] R. Albanese and G. Rubinacci. Solution of three dimensional eddy current problems by integral and differential methods.IEEE Trans. Magn., vol. 24(1):98–101, 1988 1988

[2] Alonso Rodr´ ıguez and A 2010

[3] A. Buffa, M. Costabel, and D. Sheen. On traces for H(curl, Ω) in Lipschitz domains. J. Math. Anal. Appl., 276(2):845–867, 2002 2002

[4] C. R. Dohrmann. A preconditioner for substructuring based on constrained energy minimization.SIAM J. Sci. Comput., 25(1):246–258, 2003 2003

[5] C. R. Dohrmann and O. B. Widlund. A BDDC algorithm with deluxe scaling for three-dimensional H(curl) problems.Comm. Pure Appl. Math., 69(4):745–770, 2016 2016

Receipt and verification

First computed	2026-05-20T00:01:09.354485Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

413155fb5127d5802391c50d598bb15f4f241015b4b50ba321422ed32e3fa822

Aliases

arxiv: 2605.15636 · arxiv_version: 2605.15636v1 · doi: 10.48550/arxiv.2605.15636 · pith_short_12: IEYVL62RE7KY · pith_short_16: IEYVL62RE7KYAI4R · pith_short_8: IEYVL62R

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IEYVL62RE7KYAI4RYUGVTC5RL5 \
  | 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: 413155fb5127d5802391c50d598bb15f4f241015b4b50ba321422ed32e3fa822

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9325261ccad91ae38cb92fd145fb250922c6d645822bfcaf64fb708894e576c6",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-15T05:41:57Z",
    "title_canon_sha256": "d9a95e40b4eea80e8777f8241862b60f3f22b3db9a1e1b002cc305825b1f5132"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15636",
    "kind": "arxiv",
    "version": 1
  }
}