Novel formulation for the scalar-field approach of IE-MEI method to solve the three-dimensional scattering problem
A novel formulation for the Scalar-field approach of Integral Equation formulation of the Measured Equation of In-variance (SIE-MEI) is derived from the scalar reciprocity relation to solve the scalar Helmholtz equation. The basics of this formulation are similar to IE-MEI method for the electromagnetic (EM) problem. The surface integral equation is derived from reciprocity relation and on-surface MEI postulates are used. As a result it generates a sparse linear system with the same number of unknowns as of Boundary Element Method (BEM) and keeps the merits in minimum storage memory requirements and CPU time consumption for computing the final matrix. IE-MEI method has been proposed for two-dimensional (2D) electromagnetic problem, but three-dimensional (3D) problem is very difficult to be extend. This scalar-field approach of IE-MEI method is identical to electromagnetic in 2D, but easily extended to the 3D scalar-field scattering problem contrary to EM problem. The numerical results of sphere and cube are verified with some rigorous or numerical solutions, which give excellent agreement.
ie-mei sie-mei scalar reciprocity relation 3d acoustic problem numerical technique for 3d scattering problem