Abstract: A fast direct method for the solution of structured linear systems of equations. A linear system with a matrix that possesses larger submatrices that are of low ranck (to some precision).

Abstract: A computer program product, an apparatus, and a method for modeling equivalent surface sources on a closed, arbitrarily shaped object that result from the imposition of an arbitrary time-harmonic incident field (e.g., a radar wave) are provided. An object divided into by a plurality of patches 302 and parameters for the incident field and the properties of the object 304 are provided to the system. Next, the system produces a discretized representation of a well-conditioned boundary integral equation in the form of a well-conditioned matrix equation, modeling the interaction between the incident field and the object 306. The well-conditioned linear system is solved numerically to determine equivalent surface sources on the object 308. The equivalent sources may then be used to determine electromagnetic fields resulting therefrom 310. The invention provides improved computational efficiency as well as increased modeling accuracy by effectively reducing the numerical precision necessary.

Abstract: A machine for determining field-dependent physical characteristics contains tables of precomputed quadratures and employs them to integrate numerically over a problem boundary. The quadratures are based on products of a kernel function and a basis that spans a wide range of density functions. The kernel function is dependent on a target node's position, and different quadratures are precomputed for different target-node positions or ranges thereof. In the case of at least some of the quadratures, some the basis functions include integrable singularities. The solver divides the problem boundary into a plurality of problem intervals, to which it maps the canonical interval. To integrate a problem interval for a target point, the solver employs a precomputed quadrature that is associated with the target point's relative position and that was generated by using a basis in which a singularity occurs at each canonical-interval location that was mapped to a geometrical singularity on the problem interval.

Abstract: A computer program product, an apparatus, and a method for modeling equivalent surface sources on a closed, arbitrarily shaped object that result from the imposition of an arbitrary time-harmonic incident field (e.g., a radar wave) are provided. An object divided into by a plurality of patches 302 and parameters for the incident field and the properties of the object 304 are provided to the system. Next, the system produces a discretized representation of a well-conditioned boundary integral equation in the form of a well-conditioned matrix equation, modeling the interaction between the incident field and the object 306. The well-conditioned linear system is solved numerically to determine equivalent surface sources on the object 308. The equivalent sources may then be used to determine electromagnetic fields resulting therefrom 310. The invention provides improved computational efficiency as well as increased modeling accuracy by effectively reducing the numerical precision necessary.