A fast solver for integral equations with convolution-type Kernel

This paper studies the data redundancy of the coefficient matrix of the corresponding discrete system which forms a basis for fast algorithms of solving the integral equation whose kernel includes a convolution function factor. We develop lossless matrix compression strategies, which reduce the cost of integral evaluations and the storage to linear complexity, i.e., the same order of the approximation space dimensions. We establish that this algorithm preserves the convergence order of the approximate solution. We also propose a hardware-aware parallel algorithm for these strategies.