Calculations of radar scattering, acoustic scattering, electromagnetic interference, high frequency circuit's properties, antenna patterns, etc. often strain or are beyond the capabilities of even today's computers. Roughly half of the computer programs used in these fields are based on integral equations, and result in a large full matrix which must be stored and inverted. Wavelets can compress the matrix to reduce storage requirements. However, they are difficult to use for general geometries and at best require extensive rewiring of existing programs. An algorithm has been discovered for taking the matrix from existing computer programs and transforming it to reduce storage requirements by two orders of magnitude. This is done one block of the matrix at a time, so all of the original matrix is never stored at once, resulting in a new matrix in a wavelet like basis. Our new algorithm allows this transformation to be computed from readily available information. The transformed matrix is sparse, and the locations of the non-zero elements allows a rapid sparse inverse of the matrix to be calculated by well known methods. A solver based on this algorithm will be tested as a way to speed up existing computer programs.Anticipated Benefits/Commercial Applications: We have discovered an extremely efficient algorithm which allows the solution of wave scattering problems in realistic times with very high accuracy on objects significantly larger in size than possible with currently available methods. Our algorithm can be implemented in existing computer programs with minor changes to interface to our solver module, in a way transparent to the end user. There is no expensive retraining of the user. The wave scattering problems to which our solver module applies include radar scattering, antenna design, circuit design, acoustics whether for undersea for medical ultrasound or for nondestructive testing, synthetic array performance modeling, electromagnetic interference, etc. Our solver removes the need to rewrite each computer program to improve its speed and memory requirements.
