Abstract
In the investigation, the complex geometric domain is a concave geometrical pattern. Due to the symmetric character, the left side of the geometric pattern, i.e. the L-shaped region is calculated in the study. The governing equation is expressed with Laplace equations. And the analysis is solved by eigenfunction expansion and point-match method. Besides, visual C++ helps obtain the results of numerical calculation. The local values and the mean values of the function are also discussed in this study.
Highlights
The Laplace equations show an important role in the applied mathematical researches and analysis
The governing equation is expressed with Laplace equations
The analysis is solved by eigenfunction expansion and point-match method
Summary
The Laplace equations show an important role in the applied mathematical researches and analysis. Alliney [1] presented the two-dimensional potential flows to solve the Laplace’s equation with appropriate regularity conditions at infinity. Zanger [3] presented the analysis of the boundary element method applied to Laplace’s equation for the experiments involving solving the two-dimensional Laplace problem exterior to a circle and square, using both the direct and indirect methods. The EFG method with linear approximation and penalty functions to treat the essential boundary condition is used in his paper Both methods are compared for solving Laplace equation. The present paper, will analyze a symmetric domain with complex Laplace equations under two kinds of boundary conditions in order to find local values and the mean values of the function. It is hoped that the results can be further applied in engineering and technology, for example, the problem of fluid flow and heat conduction
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