---
OA_place: repository
OA_type: green
_id: '17462'
abstract:
- lang: eng
  text: We are interested in numerical algorithms for computing the electrical field
    generated by a charge distribution localized on scale l in an infinite heterogeneous
    correlated random medium, in a situation where the medium is only known in a box
    of diameter L >>l around the support of the charge. We show that the algorithm
    in [J. Lu, F. Otto, and L. Wang, Optimal Artificial Boundary Conditions Based
    on Second-Order Correctors for Three Dimensional Random Ellilptic Media, preprint,
    arXiv:2109.01616, 2021], suggesting optimal Dirichlet boundary conditions motivated
    by the multipole expansion [P. Bella, A. Giunti, and F. Otto, Comm. Partial Differential
    Equations, 45 (2020), pp. 561–640], still performs well in correlated media. With
    overwhelming probability, we obtain a convergence rate in terms of l, L, and the
    size of the correlations for which optimality is supported with numerical simulations.
    These estimates are provided for ensembles which satisfy a multiscale logarithmic
    Sobolev inequality, where our main tool is an extension of the semigroup estimates
    in [N. Clozeau, Stoch. Partial Differ. Equ. Anal. Comput., 11 (2023), pp. 1254–1378].
    As part of our strategy, we construct sublinear second-order correctors in this
    correlated setting, which is of independent interest.
acknowledgement: We would like to thank our affiliations, Institute of Science and
  Technology Austria and Max Planck Institute for Mathematics in the Sciences, for
  supporting the authors’ visits to each other, which greatly facilitated this work.
  We would like to thank Marc Josien and Quinn Winters for assistance in numerical
  implementation.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicolas
  full_name: Clozeau, Nicolas
  id: fea1b376-906f-11eb-847d-b2c0cf46455b
  last_name: Clozeau
- first_name: Lihan
  full_name: Wang, Lihan
  last_name: Wang
citation:
  ama: Clozeau N, Wang L. Artificial boundary conditions for random elliptic systems
    with correlated coefficient field. <i>Multiscale Modeling and Simulation</i>.
    2024;22(3):973-1029. doi:<a href="https://doi.org/10.1137/23M1603819">10.1137/23M1603819</a>
  apa: Clozeau, N., &#38; Wang, L. (2024). Artificial boundary conditions for random
    elliptic systems with correlated coefficient field. <i>Multiscale Modeling and
    Simulation</i>. Society for Industrial and Applied Mathematics. <a href="https://doi.org/10.1137/23M1603819">https://doi.org/10.1137/23M1603819</a>
  chicago: Clozeau, Nicolas, and Lihan Wang. “Artificial Boundary Conditions for Random
    Elliptic Systems with Correlated Coefficient Field.” <i>Multiscale Modeling and
    Simulation</i>. Society for Industrial and Applied Mathematics, 2024. <a href="https://doi.org/10.1137/23M1603819">https://doi.org/10.1137/23M1603819</a>.
  ieee: N. Clozeau and L. Wang, “Artificial boundary conditions for random elliptic
    systems with correlated coefficient field,” <i>Multiscale Modeling and Simulation</i>,
    vol. 22, no. 3. Society for Industrial and Applied Mathematics, pp. 973–1029,
    2024.
  ista: Clozeau N, Wang L. 2024. Artificial boundary conditions for random elliptic
    systems with correlated coefficient field. Multiscale Modeling and Simulation.
    22(3), 973–1029.
  mla: Clozeau, Nicolas, and Lihan Wang. “Artificial Boundary Conditions for Random
    Elliptic Systems with Correlated Coefficient Field.” <i>Multiscale Modeling and
    Simulation</i>, vol. 22, no. 3, Society for Industrial and Applied Mathematics,
    2024, pp. 973–1029, doi:<a href="https://doi.org/10.1137/23M1603819">10.1137/23M1603819</a>.
  short: N. Clozeau, L. Wang, Multiscale Modeling and Simulation 22 (2024) 973–1029.
corr_author: '1'
date_created: 2024-08-25T22:01:08Z
date_published: 2024-09-01T00:00:00Z
date_updated: 2025-09-08T09:01:00Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/23M1603819
ec_funded: 1
external_id:
  arxiv:
  - '2309.06798'
  isi:
  - '001285416500001'
intvolume: '        22'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2309.06798
month: '09'
oa: 1
oa_version: Preprint
page: 973-1029
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
  call_identifier: H2020
  grant_number: '948819'
  name: Bridging Scales in Random Materials
publication: Multiscale Modeling and Simulation
publication_identifier:
  eissn:
  - 1540-3467
  issn:
  - 1540-3459
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Artificial boundary conditions for random elliptic systems with correlated
  coefficient field
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 22
year: '2024'
...
---
_id: '6762'
abstract:
- lang: eng
  text: "We present and study novel optimal control problems motivated by the search
    for photovoltaic materials with high power-conversion efficiency. The material
    must perform the first step: convert light (photons) into electronic excitations.
    We formulate various desirable properties of the excitations as mathematical control
    goals at the Kohn-Sham-DFT level\r\nof theory, with the control being given by
    the nuclear charge distribution. We prove that nuclear distributions exist which
    give rise to optimal HOMO-LUMO excitations, and present illustrative numerical
    simulations for 1D finite nanocrystals. We observe pronounced goal-dependent features
    such as large electron-hole separation, and a hierarchy of length scales: internal
    HOMO and LUMO wavelengths < atomic spacings < (irregular) fluctuations of the
    doping profiles < system size."
article_processing_charge: No
arxiv: 1
author:
- first_name: Gero
  full_name: Friesecke, Gero
  last_name: Friesecke
- first_name: Michael
  full_name: Kniely, Michael
  id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
  last_name: Kniely
  orcid: 0000-0001-5645-4333
citation:
  ama: Friesecke G, Kniely M. New optimal control problems in density functional theory
    motivated by photovoltaics. <i>Multiscale Modeling and Simulation</i>. 2019;17(3):926-947.
    doi:<a href="https://doi.org/10.1137/18M1207272">10.1137/18M1207272</a>
  apa: Friesecke, G., &#38; Kniely, M. (2019). New optimal control problems in density
    functional theory motivated by photovoltaics. <i>Multiscale Modeling and Simulation</i>.
    SIAM. <a href="https://doi.org/10.1137/18M1207272">https://doi.org/10.1137/18M1207272</a>
  chicago: Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density
    Functional Theory Motivated by Photovoltaics.” <i>Multiscale Modeling and Simulation</i>.
    SIAM, 2019. <a href="https://doi.org/10.1137/18M1207272">https://doi.org/10.1137/18M1207272</a>.
  ieee: G. Friesecke and M. Kniely, “New optimal control problems in density functional
    theory motivated by photovoltaics,” <i>Multiscale Modeling and Simulation</i>,
    vol. 17, no. 3. SIAM, pp. 926–947, 2019.
  ista: Friesecke G, Kniely M. 2019. New optimal control problems in density functional
    theory motivated by photovoltaics. Multiscale Modeling and Simulation. 17(3),
    926–947.
  mla: Friesecke, Gero, and Michael Kniely. “New Optimal Control Problems in Density
    Functional Theory Motivated by Photovoltaics.” <i>Multiscale Modeling and Simulation</i>,
    vol. 17, no. 3, SIAM, 2019, pp. 926–47, doi:<a href="https://doi.org/10.1137/18M1207272">10.1137/18M1207272</a>.
  short: G. Friesecke, M. Kniely, Multiscale Modeling and Simulation 17 (2019) 926–947.
date_created: 2019-08-04T21:59:21Z
date_published: 2019-07-16T00:00:00Z
date_updated: 2025-07-10T11:53:49Z
day: '16'
department:
- _id: JuFi
doi: 10.1137/18M1207272
external_id:
  arxiv:
  - '1808.04200'
  isi:
  - '000487931800002'
intvolume: '        17'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1808.04200
month: '07'
oa: 1
oa_version: Preprint
page: 926-947
publication: Multiscale Modeling and Simulation
publication_identifier:
  eissn:
  - 1540-3467
  issn:
  - 1540-3459
publication_status: published
publisher: SIAM
quality_controlled: '1'
scopus_import: '1'
status: public
title: New optimal control problems in density functional theory motivated by photovoltaics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 17
year: '2019'
...