Cost‐efficient numerical algorithm for solving the linear inverse problem of finding a variable magnetization

Abstract

The paper is devoted to developing an original cost‐efficient algorithm for solving the inverse problem of finding a variable magnetization in a rectangular parallelepiped. The problem is ill‐posed and is described by the integral Fredholm equation.It is shown that after discretization of the area and approximation of the integral operator, this problem is reduced to solving a system of linear algebraic equations with the Toeplitz‐block‐Toeplitz matrix. We have constructed the memory efficient variant of the stabilized biconjugate gradient method BiCGSTABmem. This optimized algorithm exploits the special structure of the matrix to reduce the memory requirements and computing time.The efficient implementation is developed for multicore CPU and GPU. A series of the model problems with synthetic and real magnetic data are solved. Investigation of efficiency and speedup of parallel algorithm is performed.