2018•Lobachevskii Journal of MathematicsRequires access

Solution of Nonhomogeneous Helmholtz Equation with Variable Coefficient Using Boundary Domain Integral Method

Р. Ф. Марданов, S. K. Zaripov

Abstract

The Boundary Domain Integral Method (BDIM) is applied to the solution of the nonhomogeneous Helmholtz equation with variable coefficient. The analytical formulas for the integrals over the individual boundaries and domain integrals are used to increase the accuracy of the numerical approach. Comparisons of the developed BDIM with the analytical solutions for the homogeneous Helmholtz equation with constant coefficient and the nonhomogeneous Helmholtz equation with variable coefficient are given.

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Key concepts: Helmholtz equation, Mathematics, Helmholtz free energy, Mathematical analysis, Electric-field integral equation, Integral equation, Domain (mathematical analysis), Variable (mathematics)