Memory-efficient Algorithm for the Reverse issue of  Variable Density
Elena N. Akimova, Vladimir E. Misilov, and Maxim S. Arguchinsky
Electronic Devices, Vol. 13, No. 2, 2024.
DOI: https://doi.org/10.6025/ed/2024/13/2/49-56
Link: https://www.dline.info/ed/fulltext/v13n2/edv13n2_2.pdf
Abstract:
A memory-efficient algorithm is developed and implemented to address the reverse issue of determining the variable density within a curvilinear layer from gravitational information. This algorithm is structured around the stabilized bi-conjugated gradient approach. By approximating the SLAE matrix with a Toeplitz-block-Toeplitz structure, the modification dramatically lowers the need for memory. The parallel versions of the algorithm were created for the Uran supercomputer, utilizing a combination of MPI+OpenMP technology. The practicality of this algorithm was demonstrated through its successful application to a model problem featuring synthetic data.