Pith Number

pith:SYBTEFJY

pith:2026:SYBTEFJYOGX5U7MEJIAVFHTTDH

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Goal-Oriented Time Adaptivity for Linear Port-Hamiltonian Differential-Algebraic Equations of Index~1

Aashutosh Sharma, Andreas Bartel, Manuel Schaller

Goal-oriented time adaptivity controls energy balance violations in linear port-Hamiltonian DAEs of index 1.

arxiv:2605.14082 v1 · 2026-05-13 · math.NA · cs.NA

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Claims

C1strongest claim

We propose an approach that controls the energy balance violation for port-Hamiltonian differential algebraic equations via time adaptivity using a posteriori grid refinement techniques based on the dual weighted residual method.

C2weakest assumption

The port-Hamiltonian structure can be leveraged to efficiently compute the error estimators using a dissipativity-exploiting block-Jacobi approximation that remains accurate enough for the target goal-oriented error control.

C3one line summary

A new adaptive time-stepping method for port-Hamiltonian DAEs controls energy balance errors via dual-weighted residual refinement and structure-exploiting approximations, demonstrated on circuit models.

References

27 extracted · 27 resolved · 0 Pith anchors

[1] Springer Basel AG, 2003 2003

[2] Goal-oriented time adaptivity for port-Hamiltonian systems 2025

[3] Port-Hamiltonian systems modelling in electrical engineering, 2023 2023

[4] Port-Hamiltonian descriptor systems.Mathematics of Control, Signals, and Systems, 30(4), 2018 2018

[5] An optimal control approach to a posteriori error estimation in finite element methods.Acta Numerica, 10:1–102, 2001 2001

Formal links

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Receipt and verification

First computed	2026-05-17T23:39:12.299679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

960332153871afda7d844a01529e7319cd6ddca3f0dc9977e699d6d3ffd64001

Aliases

arxiv: 2605.14082 · arxiv_version: 2605.14082v1 · doi: 10.48550/arxiv.2605.14082 · pith_short_12: SYBTEFJYOGX5 · pith_short_16: SYBTEFJYOGX5U7ME · pith_short_8: SYBTEFJY

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/SYBTEFJYOGX5U7MEJIAVFHTTDH \
  | 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: 960332153871afda7d844a01529e7319cd6ddca3f0dc9977e699d6d3ffd64001

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98b40b277cf8fc3a3df44269c57bc9055b0f492877f38be4e5063ae689fda9bf",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T20:07:58Z",
    "title_canon_sha256": "3737fd90e0e760e6fc9df342fd53a1daf90e6b146604a29dfa6e338bd3dd26dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14082",
    "kind": "arxiv",
    "version": 1
  }
}