Patent Document ID: 7844407
Application ID: 12215034
Patent Flag: 1

Claim One:
1. A computer-implemented method for determining the unknown physical sources of an object arising from a physical excitation of the object that produces the sources, the object having associated therewith a system interaction matrix, Z, that is characteristic of the object and that depends on the object's geometry, comprising: determining source locations from a geometry of the object stored in a tangible memory of the computer; ordering and grouping the source locations according to their distance from a reference point so that factors of the system interaction matrix can be approximated by blocks of low rank; logically partitioning the memory in a compressed outer product form to partition the system interaction matrix into 9 or more blocks, Z ij , so that the diagonal blocks are square and a dimension of a block corresponds to a number of unknown source locations in a group, the logical partition created without computing Z ij ; for the partition chosen, computing terms of a Lower Upper (LU) factorization of the partitioned system interaction matrix, wherein the LU factors are chosen to have the following relationship: ⁢ U ij = Z ij - ∑ p = 1 i - 1 ⁢ L ip ⁢ U pj L ij = Dinv jj ⁡ ( Z ij - ∑ p = 1 j - 1 ⁢ L ip ⁢ U pj ) ⁢ i , j = 1 , 2 , … ⁢ , n > 2 and wherein terms of the L and U blocks of this factorization are computed and stored in a compressed outer product form and where Dinv ij are computed by LU factorization, computing and storing the factorization in the logically partitioned memory in a compressed outer product form to substantially reduce a number of computations and memory space required to determine the physical sources; determining the physical sources, J i from terms of the compressed L and U factors, wherein the physical sources and the physical excitations, V i , have the following relationship: Y i = V i - ∑ j = 1 i - 1 ⁢ L ij ⁢ Y i i = 1 , 2 , … ⁢ , n J i = Dinv u ⁡ ( Y i - ∑ j = i + 1 n ⁢ U ij ⁢ J j ) i = n , n - 1 , … ⁢ , 1.