A NUMERICAL COORDINATE TRANSFORMATIONFOR EFFICIENT EVALUATION OF OSCILLATORY INTEGRALS OVER WAVE BOUNDARY ELEMENTS

摘要

When the Partition of Unity Method is ap-plied to a discretised integral equation form of the Helmholtzoperator, the computational cost is dominated by the evalu-ation of highly oscillatory integrals over discretisations. Thispaper presents a new numerical approach that is based on acoordinate transformation to a secondary discretisation thatis aligned with an approximation to the curvilinear coordinatein which oscillation is taking place. This transforms a 2D sur-face integral into an equivalent set of 1D integrals that may beevaluated cheaply yet accurately. A method is proposed fordealing efficiently with difficulties that occurred at the edgesof elements in previous work.