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The goal of the project is is to investigate properties of solutions of equations arising in acoustics and electromagnetism, and developing, applying and theoretical understanding new effective methods of solution for these equations. Dependence of solutions of the differential equations with absorbing boundary conditions on the boundary conditions, the shape and the location of the artificial boundary will be investigated. Existence and smoothness of solutions of the integral equations arising in interior source methods will be analysed. Error estimates will be obtained and the amount of work needed to solve the equations with various methods will be assessed. Fast solvers will be studied for the linear systems of equations obtained and numerical experiments will be performed. |