Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea

Silalahi, Fitriani Tupa R.; Budhi, Wono Setya; Adytia, Didit; Groesen, E. van

doi:10.1063/1.4930628

Cited by 2 publications

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“…The third boundary value problem of Laplace's equation is studied by using functional variations, and it is proved to be equivalent to an extreme value problem of functional variations in literature [2]; the third boundary value problem of Laplace equation is studied with an example of ship motion at sea, and its numerical solution is given in literature [3]; a Monte Carlo method for solving the third boundary value problem of Laplace's equation is proposed in literature [4]; the algorithm provides a possibility to construct unbiased estimators of solutions. However, the research on the analytical solution of the third boundary value problem of Laplace's equation has not been mentioned in the relevant literature.…”

Section: Introductionmentioning

confidence: 99%

Solution of the Third Kind Boundary Value Problem of Laplace’s Equation Based on Conformal Mapping

Fu-qian¹

2019

JAMP

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In order to overcome the difficulty in solving the boundary value problem of electrostatic field with complex boundary and to give a new method for solving the third boundary value problem of Laplace's equation, in this paper, the third boundary value problem of Laplace's equation is studied by combining conformal mapping with theoretical analysis, the several analytical solutions of third boundary value problems of Laplace's equation are gives, the correctness of its solution is verified through computer numerical simulation, and a new idea and method for solving the third boundary value problem of Laplace's equation is obtained. In this paper, the boundary condition of the solving domain is changed by the appropriate conformal mapping, so that the boundary value problem on the transformed domain is easy to be solved or be known, and then the third kind boundary value of the Laplace's equation can be solved easily; its electric potential distribution is known. Furthermore, the electric field line and equipotential line are plotted by using the MATLAB software.

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Section: Introductionmentioning

confidence: 99%

Solution of the Third Kind Boundary Value Problem of Laplace’s Equation Based on Conformal Mapping

Fu-qian¹

2019

JAMP

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Numerical solution of Laplace equation for ship problem in the sea using finite difference method

Silalahi

Dirgayussa

2016

AIP Conference Proceedings

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Numerical solution for Laplace equation with mixed boundary condition for ship problem in the sea

Cited by 2 publications

References 1 publication

Solution of the Third Kind Boundary Value Problem of Laplace’s Equation Based on Conformal Mapping

Solution of the Third Kind Boundary Value Problem of Laplace’s Equation Based on Conformal Mapping

Numerical solution of Laplace equation for ship problem in the sea using finite difference method

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