Pith Number

pith:3LNA6NI5

pith:2026:3LNA6NI5KSNEX4BVIX7JGYJDYW

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A Parallel and Adaptive Mesh-Free method for Heterogeneous Porous Media

Kapil Chawla, Sanghyun Lee, Yeonjong Shin

Normalized radial basis functions with Shepard stabilization approximate discontinuous step functions to arbitrarily small L1 error.

arxiv:2605.16564 v1 · 2026-05-15 · math.NA · cs.NA

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\pithnumber{3LNA6NI5KSNEX4BVIX7JGYJDYW}

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We provide a theoretical analysis showing that the proposed normalized RBF framework achieves arbitrarily small L^1 error in approximating discontinuous step functions.

C2weakest assumption

Shepard normalization stabilizes the RBF approximation near sharp interfaces so that sparse regression can produce robust continuous representations of the original discontinuous data.

C3one line summary

PAM is a mesh-independent RBF framework with Shepard normalization, sparse regression, adaptive refinement, and subdomain parallelism that approximates discontinuous data with arbitrarily small L1 error for step functions.

References

31 extracted · 31 resolved · 0 Pith anchors

[1] Bear, Dynamics of Fluids in Porous Media, Elsevier, 1972 1972

[2] Dagan, Flow and Transport in Porous Formations, Springer, 1989 1989

[3] L. J. Durlofsky, Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media, Water Resources Research 27 (5) (1991) 699–708. 24 1991

[4] T. Y . Hou, X.-H. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media, Journal of computational physics 134 (1) (1997) 169–189 1997

[5] Y . Efendiev, T. Y . Hou, Multiscale finite element methods: theory and applications, V ol. 4, Springer Science & Business Media, 2009 2009

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:29.349903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dada0f351d549a4bf03545fe936123c5b6e8902dd8c50da22a641654a3c1b217

Aliases

arxiv: 2605.16564 · arxiv_version: 2605.16564v1 · doi: 10.48550/arxiv.2605.16564 · pith_short_12: 3LNA6NI5KSNE · pith_short_16: 3LNA6NI5KSNEX4BV · pith_short_8: 3LNA6NI5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3LNA6NI5KSNEX4BVIX7JGYJDYW \
  | 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: dada0f351d549a4bf03545fe936123c5b6e8902dd8c50da22a641654a3c1b217

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8909193c6ae15b737e76e871ac2ca76f527ae6ef0526ffac47d58576cbb70a06",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-15T19:07:29Z",
    "title_canon_sha256": "918b6cd8ecd61bf121411e5e004de059e570b52a021c8b52ba4e74091708d2c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16564",
    "kind": "arxiv",
    "version": 1
  }
}