In this paper, a system of equation for mixed Boundary Value Problem (BVP) on a square shape domain is proposed. We apply Boundary Element Method (BEM) to form a system of equations of two dimensional potential problem which satisfies Laplace equation. The mixed BVP will be reduced to Boundary Integral Equation (BIE) by using direct method which involve Green second identity representation formula. Boundary of the square shape domain is discretized into four linear boundary elements. Each of element is prescribed with specific BC value where Neumann BC is prescribed on one element of the boundary and Dirichlet BC on the other three elements of the boundary. Then, linear interpolation is used on the discretized element. However, there can be two values of Neumann BC at a corner node due to discontinuous outward normal. While, there is only one unknown value for Dirichlet BC at each node. Therefore, our first results for this considered domain yields to the underdetermined system.Hence, .....

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The aim of this research is to produce the system of equations for three different mixed Boundary Value Problems (BVPs). The potential problem which involves the Laplace’s equation on a square shape domain was considered, where the boundary is divided into four sets of linear boundary elements. The Boundary Element Method (BEM) was used to approximate the solutions for BVP. The mixed BVPs were reduced to Boundary Integral Equation (BIEs) by using direct method which were related with Green’s second identity representation formula. Then, linear interpolation was used on the discretized elements. The results showed that, there are three system of equations which were obtained. For some cases of mixed BVPs which involves discontinuous fluxes problems yields underdetermined systems. Out of the three problems that being considered, one of three BVPs leads to the underdetermined system of equations. Therefore, the transformation for the underdetermined system to the standard form is nece.....

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Boundary Element Method (BEM) is a numerical way to approximate the solutions of a Boundary Value Problem (BVP). The potential problem which involves the Laplace's equation on the square shape domain will be considered where the boundary is divided into four sets of linear boundary elements. We study the derivation system of equation for mixed BVP with one Dirichlet Boundary Condition (BC) is prescribed on one element of the boundary and Neumann BC on the other three elements. The mixed BVP will be reduced to a Boundary Integral Equation (BIE) by using a direct method which involves Green's second identity representation formula. Then, linear interpolation is used where the boundary will be discretized into some linear elements. As the result, we then obtain the system of linear equations. In conclusion, the specific element in the mixed BVP will have the specific prescribe value depends on the type of boundary condition. For Dirichlet BC, it has only one value at each node but for the.....

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