Tampere University of Technology

TUTCRIS Research Portal

Geometric solution strategy of Laplace problems with free boundary

Research output: Contribution to journalArticleScientificpeer-review

Standard

Geometric solution strategy of Laplace problems with free boundary. / Poutala, Arto; Tarhasaari, Timo; Kettunen, Lauri.

In: International Journal for Numerical Methods in Engineering, Vol. 105, No. 10, 09.03.2016, p. 723-746.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Poutala, A, Tarhasaari, T & Kettunen, L 2016, 'Geometric solution strategy of Laplace problems with free boundary', International Journal for Numerical Methods in Engineering, vol. 105, no. 10, pp. 723-746. https://doi.org/10.1002/nme.4988

APA

Poutala, A., Tarhasaari, T., & Kettunen, L. (2016). Geometric solution strategy of Laplace problems with free boundary. International Journal for Numerical Methods in Engineering, 105(10), 723-746. https://doi.org/10.1002/nme.4988

Vancouver

Poutala A, Tarhasaari T, Kettunen L. Geometric solution strategy of Laplace problems with free boundary. International Journal for Numerical Methods in Engineering. 2016 Mar 9;105(10):723-746. https://doi.org/10.1002/nme.4988

Author

Poutala, Arto ; Tarhasaari, Timo ; Kettunen, Lauri. / Geometric solution strategy of Laplace problems with free boundary. In: International Journal for Numerical Methods in Engineering. 2016 ; Vol. 105, No. 10. pp. 723-746.

Bibtex - Download

@article{fed2500ed9f1456fba2e0c495e9052ed,
title = "Geometric solution strategy of Laplace problems with free boundary",
abstract = "This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples.",
keywords = "Bernoulli problem, Cauchy condition, Differential equations, Elliptic partial differential equations, Equipotential layers, Field lines, Inverse problem, Laplace problem, Mean curvature, Shape design",
author = "Arto Poutala and Timo Tarhasaari and Lauri Kettunen",
year = "2016",
month = "3",
day = "9",
doi = "10.1002/nme.4988",
language = "English",
volume = "105",
pages = "723--746",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "Wiley",
number = "10",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Geometric solution strategy of Laplace problems with free boundary

AU - Poutala, Arto

AU - Tarhasaari, Timo

AU - Kettunen, Lauri

PY - 2016/3/9

Y1 - 2016/3/9

N2 - This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples.

AB - This paper introduces a geometric solution strategy for Laplace problems. Our main interest and emphasis is on efficient solution of the inverse problem with a boundary with Cauchy condition and with a free boundary. This type of problem is known to be sensitive to small errors. We start from the standard Laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another. This results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of Laplace's problem. Interpretation in terms of a geometric flow will provide us with stability considerations. The approach is demonstrated with several examples.

KW - Bernoulli problem

KW - Cauchy condition

KW - Differential equations

KW - Elliptic partial differential equations

KW - Equipotential layers

KW - Field lines

KW - Inverse problem

KW - Laplace problem

KW - Mean curvature

KW - Shape design

U2 - 10.1002/nme.4988

DO - 10.1002/nme.4988

M3 - Article

VL - 105

SP - 723

EP - 746

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 10

ER -