Compression in 3-D integral equation modeling

The integral equations (IE) method is a powerful tool for forward electromagnetic (EM) modeling. However, due to a dense matrix arising from the IE formulation, practical application of the IE method is limited to modeling of relatively small bodies. The use of a compression technique can overcome this limitation. The compression transformation is formulated as a multiplication by a compression matrix. Using this matrix as a preconditioner to an integral equation, we convert the originally dense matrix of the problem to a sparse matrix, which reduces its size and speeds up computations. Thus, compression helps to overcome practical limitations imposed on the numerical size of the anomalous domain in IE modeling. With the compression, the flexibility of the IE method approaches that of finite-difference (FD) or finite-element (FE) methods, allowing modeling of large-scale conductivity variations.