{
  "abstract": "We consider a transport problem motivated by freeform optical design of a parallel-to-far-field reflector. Classical formulations rely on either elliptic or hyperbolic Monge--Ampère equations, leading to globally convex/concave or saddle-shape reflector geometries, respectively. However, the design of smooth reflector arrays may require optical surfaces combining both types of curvature. To address this, we introduce a mixed elliptic--hyperbolic Monge--Ampère system obtained by partitioning the source domain into one elliptic and one hyperbolic subregion, and we develop a least-squares method for its numerical approximation. Numerical examples demonstrate the ability of the proposed framework to compute both isolated and periodic mixed-type transport solutions, yielding smooth reflector configurations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23544",
  "author_total": 6,
  "authors": [
    {
      "name": "G. V. Carvalho"
    },
    {
      "name": "M. J. H. Anthonissen"
    },
    {
      "name": "J. H. M. ten Thije Boonkkamp"
    },
    {
      "name": "L. Kusch"
    },
    {
      "name": "K. Mitra"
    },
    {
      "name": "W. L. IJzerman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2mcw13wd2wx89.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23544",
  "fulltext_url": null,
  "id": "2mcw13wd2wx89",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23544",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7222951047",
  "pdf_url": "https://arxiv.org/pdf/2610.23544",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2mcw13wd2wx89.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.23544",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23544"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Mixed Elliptic--Hyperbolic Monge--Ampère Problem: Modeling and a Least-Squares Solver",
  "title_text": "A Mixed Elliptic--Hyperbolic Monge--Ampère Problem: Modeling and a Least-Squares Solver",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/2mcw13wd2wx89",
  "venue": "arXiv",
  "versions": []
}